Partial differentiation Definition and 125 Threads

Homework Statement Need to find the tangent to the curve at: e^(xy) + x^2*y - (y-x)^2 + 3 I just implicitly differentiate the expression to find the gradient and then use the points given to find the equation, right? Or does this involve partial differentiation? Homework Equations...

Homework Statement Let x=ts^2 -1 and y=ln(s)-t Use the chain rule for functions of two variables to determine ∂f/∂t at (s,t)=(1,1) The Attempt at a Solution y=ln(s)-t ∂f/∂t= ∂f/∂s X ∂s/∂t -1 t=x+1/s^2 ∂t/∂s= -2(x+1)/s^3 ∂s/∂t=s^3/-2(x+1) ∴ ∂f/∂t= s^2/-2(x+1)...

Homework Statement (x,y) = x√(xy) The answer says: fx=3/2*√(xy) fy=(x√x) / (2√y) fxx= (3√y) / (4√x) fxy= (3√x) / (4√y) fyx =(3√x) / (4√y) fyy = -(x√x) / (4y√ I don't get from the beginning. shouldnt fx be equal to (3/2)x^2 * (x^3 * y)^-(3/2)?? When I do second derivative fxx from fx, it...

I have x=x(t) and y=y(t) and I'm working in polar co-ordinates so $$x=rcos{\theta}$$ and $$y=rsin{\theta}$$. I want to find ${\theta}'(t)$ so by the chain rule I want $${\theta}'(x)*x'(t)+{\theta}'(y)*y'(t)$$. I know $${\theta}=arctan(y/x)$$ but how do I partially differentiate theta w.r.t x and y?

Homework Statement given z=yf(x^2-y^2) show that the x(∂z/∂y)+y(∂z/∂x)=xz/y The Attempt at a Solution cut it short, my ∂z/∂y= f(x^2-y^2)-2(y^2)f(x^2-y^2) ∂z/∂x=2xyf(x^2-y^2) i was able to prove that x(∂z/∂y)+y(∂z/∂x)=xz/y But i need help with partial differentiations...

I am checking my homework with mathematica, but sometimes when I write stuff like D[(x/((x^2 - y^2)^0.5)), y] , which is supposed to give me the partial derivative of x/((x^2 - y^2)^0.5) with respect to y, i get answer like: (1. x y)/(x^2 - y^2)^1.5 which is right, except for the...

I'm attaching the question and solution. I'm talking about the first part since the second part is the same just with different variables and stuff. I get what the solution is saying but: 1) What if I computed a Jacobian, with F = x^2 + xy + y^2 - z = 0 G = 2r + s - x = 0 H = r - 2s - y...

This is another problem than I've been stuck on for a long time and I tried reading and watching videos but I only find first order partial differentiation with more than two variables or higher order partial differentiation with only two variables. (I'm not calling f a variable but I am calling...

Homework Statement A question in a book has partially differentiated a function f(x,y) = x^2 + 8xy^2 + 2y^2 df/dx = 2x + 8y^2 = 0 at stationary point (eqn 1) df/dy = 16xy + 4y = 0 at stationary point (eqn 2) Homework Equations The Attempt at a Solution It then states...

Hello! I was wondering how I could find the following derivatives from the given function using Jacobian determinants. f(u,v) = 0 u = lx + my + nz v = x^{2} + y^{2} + z^{2} \frac{∂z}{∂x} = ? (I believe y is constant, but the problem does not specify) \frac{∂z}{∂y} = ? (I...

Homework Statement So using standard spherical polar co-ordinates, my notes define a sphere as r(s,t) = aCos(s)Sin(t) i + aSin(s)Sin(t) j + aCos(t) k and the normal to the surface is given by the cross product of the two partial differentials: \partialr/\partials X \partialr/dt...

Homework Statement Calculate ∂f/∂s + ∂f/∂t at s = 2, t = -1. Given: f = f(x,y) x = s - t y = s2 + t2 ∂f/∂x (3,5) = 0.06170 ∂f/∂y (3,5) = 0.06170 Homework Equations ∂f/∂s = ∂f/∂x * ∂x/∂s + ∂f/∂y * ∂y/∂s ∂f/∂t = ∂f/∂x * ∂x/∂t + ∂f/∂y * ∂y/∂t The Attempt at a Solution...

Homework Statement Hello all, New to partial derivatives. I was wondering if someone could look over my work and determine if my final step is as far as I can take the proble (ie. that will be my solution). Thanks in advance. Let the temperature of a 2D domain in polar coordinates (r...

Hi there, I'm writing a research paper and have hit a roadblock, (wikipedia did not help) and one of my collaborators sent me an e-mail that I do not understand. I am attempting to find when the following functional is stationary: T = \int\limits_{\lambda_{1}}^{\lambda_{2}}...

Homework Statement I sat my calculus exam at the end of june and of the questions on the paper required us to find the extreme values of the following equation: g\left(x,y\right) = \left(x-1\right)\left(y-1\right)\left(x^{2} + y^{2} -2\right) The Attempt at a Solution So i get...

Consider the partial differential of Q to the power of n w.r.t. x. How would you rearrange this expression so that it contains a partial derivative of Q w.r.t. x?

The coefficient of rigidity n of a wire of length L and uniform diameter is given by: n = AL/d^4 where A is a constant...If errors of +- 0.25% and +-1% are possible in measuring L and d respectively, find the maximum possible error in the calculated value of n... how do i do this...

Find ∂fxand ∂fy for: f(x,y)=(3x2+y2+2xy)1/2 i tried using the chain rule and said f(x,y) = u1/2 then ∂fu = 1/2u-1/2, ∂ux = 6x + 2 and ∂uy=2y+2 ∂fx = 1/2(3x2 + y2 + 2xy)-1/2(6x + 2) ∂fy = 1/2(3x2 + y2 + 2xy)-1/2(2y + 2) im not sure if this is correct as i don't know if I am doing the ∂ux and...

Homework Statement derive (s2t3) / (rs2t3) with respect to s The Attempt at a Solution equation becomes s2t3*(rs2t3)-1 which becomes s2t3r-1s-2t-3 then just differantiate like a polynomial? i tried this on an online partial differentiation calculator and it gave me an...

Homework Statement Given two functions F and G, I will use the following notation to indicate partial differentiation: Fx means dF/dx Gz means dG/dz (for example) I would like to develop the following two expressions. I don't want them grouped into brackets as they're now, but I have...

Homework Statement (A) \int{\frac{(v^2+2v+4)dv}{v^3+v^2+2v+4}} (B) \frac{\partial{M}}{\partial{y}}=(1-xy)^{-2} \frac{\partial{N}}{\partial{x}}=y^2+x^2(1-xy)^{-2} Homework Equations (A) How can I integrate this? (B)After getting the partial derivatives, are they equal? The Attempt...

I've tried looking online, but I haven't found the answer. For instance, when can you say (dFx/dt)=(dF/dt)x, where subscript x indicates partial differentiation with respect to x. I know that partial differentiation is pretty much always interchangeable, but what about in this case? I have a...

in partial differentiation why we have to use the jacobian?what does signifies?how does it differ from normal partial derivative? thanks

Hello, I got confused in my Classical Mechanics class (on a mathematical issue). So let L denote a function dependent on x and its derivative explicitly, such that its image is L(x,x*) (NOTE: I'm using * as the overdot-Leibniz notation for the derivative) and x is a function of t. To make...

Homework Statement Find \partial x / \partial z at the point (1, -1, -3) if the equation xz + y \ln x - x^2 + 4 = 0 defines x as a function of the two independent variables y and z and the partial derivative exists. Homework Equations The Attempt at a Solution x + y/x \partial x...

In the process of deriving .\nabla^2u(x,y). in polar coordinates I am confuse how to work through the steps. The first step from the book is to find \frac{\partial u}{\partial x} Standard partial differentiation is at follow: \frac{\partial u}{\partial x} = \frac{\partial u}{\partial r}...

Homework Statement [PLAIN]http://img408.imageshack.us/img408/7163/partialdifferent.jpg So this means differentiate w.r.t y first, so I want dz/dy, and then w.r.t x right? so I rearrange so that y=z3/3 + xz and differentiate w.r.t z to get dy/dz, and then do 1 over this which i get as...

Homework Statement When I write 'd' I mean the partial differentiation symbol 'del' here... Find dz/dx and dz/dy of: z=f(xy) I'm guessing this isn't a case of simply pretending the 'f( )' isn't there, how do I approach this problem? Homework Equations The Attempt at a Solution

I am in the middle of finding a general solution for an equation . However I am stuck here: c^2 ∫ dv/ (v^2 -c^2) = ∫ g dt I know Partial diiferentiation would be the best approach however I cannot really get started. Help appreciated Homework Equations The Attempt at a Solution

Homework Statement If z = f(x-y), show that dz/dx + dz/dy = 0 2. The attempt at a solution I thought: dz/dx = fx dz/dy = -fy which doesn't make sense really... because its not equal to 0. or maybe it should be: dz/dx = dz/df * df/dx = fx * ?? dz/dy = dz/df * df/dy = -fy * ??

I have a function z=f(xz+y) and I want to find the partial differential of z with respect to y (it's a general sort of question, I only need it in terms of the variables already given). My answer would be just partial df/dy but this isn't the right answer. I'm not too hot on partial...

Homework Statement Hey >.< another simple problem; find \frac{\partial u}{\partial y} , \frac{\partial v}{\partial y}, \frac{\partial w}{\partial y} given that u - v + 2w = x + 2z 2u + v - 2w = 2x - 2z u - v + w = z - y The Attempt at a Solution I don't know, this question is really...

Homework Statement Find \frac{\partial z}{\partial x} \frac{\partial z}{\partial y} where z=\left( [x+y]^3-4y^2 \right)^{\frac{1}{2}}Homework Equations -The Attempt at a Solution I know that \frac{\partial z}{\partial y}=\frac{3(x+y)^2-8y}{2\sqrt{(x+y)^3-4y^2}} but I am unsure whether...

Homework Statement If x = yz and y = 2sin(y+z), find dx/dy and d^2x/dy^2 Homework Equations The Attempt at a Solution I am beyond confused at how to even start this one, the problem is not like any of the examples in my book. I know x = ydz + zdy but don't know how to deal...

Homework Statement http://img94.imageshack.us/img94/3853/physicse.jpg The Attempt at a Solution I kept y fixed, and so I ended up with the following equation: Integ[dU/U] = Integ[x] And we end up with: U(x,y) = e^x * g(y) To solve g(y), we sub the solution into the 2nd PDE provided to...

I was working through this problem, I understand the method, but got stuck trying to differentiate the arc tan terms... In the table of standard derivatives, \frac{d}{dx} \arctan{x} = \frac{1}{1+x^2} and for PDE's, you treat y as constant when differentiating w.r.t. x --- Any...

Homework Statement The function f(x,y) satisfies the d.e. y{\partial f \over \partial x} + x{\partial f \over \partial y} = 0 By changing to new vars u = x^2-y^2 and v=2xy show that f is a function of x^2-y^2 only. Homework Equations \frac{\partial }{\partial x}=\frac{\partial...

Hi, I've got the following problem: Show that if z = x^nf(u) and u = y/x then x\frac{\partial{z}}{\partial{x}} + y\frac{\partial{z}}{\partial{y}} = nz I know partial differentiation fairly well, but I've never seen one laid out like this before, and am not too sure how to get started...

In fluid mechanics velocity is given in the form \textbf{V}=u\textbf{i}+v\textbf{j}+w\textbf{k} Homework Statement A two-dimensional velocity field is given by \textbf{V}=(x^2-y^2+x)\textbf{i}+(-2xy-y)\textbf{j} At (x_o,y_o) compute the accelerations a_x\text{ and }a_y I am...

Homework Statement Okay, I know that I must be overlooking the obvious here, but here goes. Take some velocity function of time and space V(x,y,z,t) and we want to find its derivative, the acceleration vector a(x,y,z,t) If we have \vec{V}=u\hat{i}+v\hat{j}+w\hat{k} Then by chain rule...

What does the subscript outside a partial differentiation mean? For example: \left(\frac{\partial x}{\partial y}\right)_z What does the z mean above?

Homework Statement I am trying to understand how some equations are obtained in some lecture notes I have. This is my starting equation-http://i423.photobucket.com/albums/pp315/skaboy607/StartEquation.png And I need to satisfy these conditions...

Homework Statement I've got a question more with the structure of how this problem is presented: If x^(sin y) = y^(cos x) Find \frac{dx}{dy}(\frac{pi}{4},\frac{pi}{4}) Homework Equations We have been taught to solve by implicit...

Hello again! This time I have another calculus question for you, coming straight out of my study of the free Schrodinger equation, since I am not that experienced with that kind of derivative. It all starts with a given wavefunction (which I think is 2-dimensional,correct me if wrong)...

I have a basic question about taking partial derivatives. Say I have a function of 3 variables and i want the derivative of only one. Do I take the derivative of the one variable and HOLD THE OTHER TWO CONSTANT? Or, do I take the derivative of the variable and TREAT THE OTHER TWO AS...

if u(x,t)=ae^-gx sin(nt-gx) where A,g and n are const.,and partial derivative of u w.r.t t= a^2[(partial derivative w.r.t x(partial derivative of u w.r.t x)] show :(1/a)[n/2]^1/2=g

given that z=[x^2 tan^-1(y/x)]-[y^2 tan^-1(x/y)].find value of [z][xy]. where [z][xy] stand for partial derivative w.r.ty(partial derivative of z w.r.tx)

Homework Statement For the function of two variables f(x,y)=tan^-1(y/x) find df/dx and df/dy I know i just differentiate with respect to x and then to y but I'm stuck on the tan^-1(y/x) I know tan^-1(x)=1/1+X^2 when I applied this with respect to x I get 1/-1+y I think this is wrong...

Homework Statement Let Δf= d^2f/dx^2+ d^g/dy^2 (laplace equation - Partial Derivatives) Show Δ(f(g(z))= Mod(g'(z))^2 * Δf(w,v) where g(z)=w(x,y)+v(x,y)i Homework Equations we propably need to use cauchy riemman equations: dw/dx = dv/dy and dw/dy = - dv/dx and chain rule The Attempt...

Homework Statement Find the partial of z with respect to x keeping r constant. Homework Equations z=x2+y2 x= rcos(t) y= rsin(t) The Attempt at a Solution= r^2(cos(t))^2 + r^2(sin(t))^2 use product rule on "x" and hold r and y constant = [0(cos(t))^2 + r^2(2cos(t))(-sin(t)))] + 0...