Implicit Definition and 520 Threads

Homework Statement I am told to find dy/dx by implicit differentiation where: e^(x^2 * y) = x + y Homework Equations The above equation and the ln of it.The Attempt at a Solution e^(x^2 * y) = x + y (x^2 * y)ln(e) = ln(x+y) x^2 * y = ln(x+y) x^2(dy/dx) + y(2x) = 1/(x+y) * (1 + dy/dx)...

Hello everybody, I´m simulating a problem of indentation of a tungsten needle tip on an aluminum layer. Before I was using just the module "Static Structural" from ANSYS, which is based on an implicit solver. Now I wanted to do the same simulation with the module "Explicit Dynamics" of ANSYS...

Homework Statement a. Given u=F(x,y,z) and z=f(x,y) find { f }_{ xx } in terms of the partial derivatives of of F. b. Given { z }^{ 3 }+xyz=8 find { f }_{ x }(0,1)\quad { f }_{ y }(0,1)\quad { f }_{ xx }(0,1) Homework Equations Implicit function theorem, chain rule diagrams, Clairaut's...

Here is the question: This is the step I came to after taking the derivatives and doing some simplification: ^ I did the work myself on paper, I just couldn't type out the whole thing clearly so that anyone else can see what I'm referring too... so I used some online tool to show that...

<< Mentor Note -- thread moved from the technical math forums at OP request, so no Homework Help Template is shown >>[/color] x2y + xy2 = 6 I know we use the chain rule from here, so wouldn't that be: (d/dx)(x2y + xy2) = (d/dx)(6) so using the chain rule of g'(x)f'(g(x) and the d/dx...

I am having trouble doing this problem from my textbook... and have no idea how to doit. 1. Homework Statement I am having trouble doing this problem from my textbook... Show that the equation x + y - z + cos(xyz) = 0 can be solved for z = g(x,y) near the origin. Find dg/dx and dg/dy (dg/dx...

Homework Statement Find y' ... X^2+y^2=25I understand (I think) implicit differentiation, but there is one issue which hangs me up. I've done this before and this is just a refresher as my last calculus course was four years ago. From what I understand, 2x+2y(y')=0 But why isn't it...

First of all thanks for the help, i have a problem finding a good explanation of de ecuation (d/dx)f=(∂f/∂x)+(∂f/∂y)*(dy/dx) could anyone write me a good explanation of this ecuation? thanks for the help

What is ##\frac{d}{dx}(\frac{x}{y^2})##? Please tell me is it correct or not: ##\frac{d}{dx}(\frac{x}{y^2}) = \frac{[\frac{d}{dx}(x)] ⋅ (y^2) - (x) ⋅ [\frac{d}{dx} (y^2)]}{(y^2)^2}## ## = \frac{(x) ⋅ (y^2) - (x) ⋅ (\frac{d}{dy} (y^2)) ⋅ \frac{dy}{dx}}{y^4}## ##= \frac{xy^2 -...

Homework Statement in the notes , 'by applying chain rule to LHS of the above equation ' , which equation is the author referring to ? it's given that f /x + (f/z)(z/x) = 0 , As we can see , the function contain variable x , y and z Homework EquationsThe Attempt at a Solution why not f /x +...

Does it make sense to say that implicit memory processes such as imprinting, priming, conditioned reflex, emotional conditioning and procedural skills are instincts? We do perform them instinctually. And I don't mean the behaviors that are a result of doing these processes. I mean the processes...

Homework Statement Find the expression for the slope on the lower half of the circle y^2 + x^2 = 25. 2. Attempt at a solution. The text says you get 2x + 2y(dy/dx) = 0. I got this and then solved for dy/dx to get dy/dx = -2y - 2x. Then, I substituted for y the x value-expression for the...

Since we have this relationship between x and y, as the two sides are equal, so are their derivatives. We just have to remember that as y is a function of x, any function of y is also a function of x, with the inner function "y" composed inside whatever is being told to do to the y. So to...

To perform implicit differentiation we must make use of the chain rule. Basically if you have a function composed in another function, its derivative is the product of the inner function's derivative and the outer function's derivative. All other rules (such as the sum rule, the product rule...

Homework Statement ∂z/∂x of ycos(xz)+(4xy)-2z^2x^3=5x[/B] Homework Equations n/a The Attempt at a Solution ∂z/∂x=(5+yz-4y+6z^2x^2)/(-yxsin(xz)-4zx^3)[/B] Is this correct? Just trying to make sure that's the correct answer. I appreciate the help. I can post my work if need be. Thanks

Hello all, Here's something I've been trying to wrap my head around: In general, it seems that integration is 'harder' than differentiation. At least analytically. Numerically it may be the other way round. For one thing, it's often easy to differentiate implicit functions. For example...

In one of the homework sheets my teacher gave us, we had to calculate area geometrically (meaning no integration was used). Some parts, she said, we needed to just eyeball which I hate doing. In this case the top left portion of a circle described by the equation...

I won't post the whole rigorous statement of the theorem, but basically the theorem states that If ##F(x,y) = 0## on a neighborhood of the form ##[x-\delta ,x+\delta ]\times [y- \epsilon ,y+\epsilon ]## and if ##\frac{\partial F(x,y)}{\partial y} \neq 0##, then there exists a function ##y=\phi...

Hello! Can someone help me with the process of solving $$\sqrt{x}$$+$$\sqrt{y}$$=5 on point (4,9)? With implicit, I differntiated both sides and ended up with 1/2x^-1/2+1/2y^-1/2$$\d{y}{x}$$=0 and I tried to isolate the dy/dx, but how do I get rid of the others? And with explicit, I isolated y...

So it has been quite a few years since I learned about implicit differentiation so the content is a bit rusty in my mind. x=rcos(θ) How do you find dx/dt? I know the answer but I am trying to figure out why. I mean dx/dt can be written as (dx/dθ)*(dθ/dt) so why is the answer not just...

Homework Statement Integrate $$v = \sqrt{2g\frac{T-v \pi r^2t}{\pi R^2}}$$ where g,T,r,R are constants Homework Equations N/A The Attempt at a Solution I tried playing around with the variables, but I am not sure how to integrate this. Just give me a little bit of hint would do. Thanks!

Hi! I recently came upon this problem : the height of a right angled triangle is increasing at a rate of 5cm/min while the area is constant. How fast must the base be decreasing at the moment when the height is 5 times the base? I drew a picture of the triangle, labelled the height (h) and...

If $y^2+\cos(x+y) = 1$ find $\frac{dy}{dx}$. How do I differentiate $\cos(x+y)$ bit?

Good Day Let's say I have developed a new method to extract, more efficiently (yes, "more efficiently" is ill-defined; but bear with me) the differential equations that describe a specific phenomena (please just assume it). So now I have a system of coupled second order differential...

Mod note: Moved from the Homework section 1. Homework Statement This might seem like a stupid question but I'm unsure what z= ƒ(x/y) means? I'm not sure how I would find ∂z/∂x , ∂z/∂y just from this statement either. Thank you Homework EquationsThe Attempt at a Solution

Is there any research that was done on animal long and short term memories? And short of empirical analysis, if there is none, is there much we could conclude, based purely on what we know about their brains? For example, from knowing which brain parts deal with explicit and which with...

Homework Statement Homework Equations The Attempt at a Solution Note: by real solution I mean the correct implicit derivative, not an actual real solution... Please help![/B]

1. Given the function ##xy+cos y+6xy^2=0## , it follows that ## dy/dx=-y/x-siny+12xy##2. My problem is how do we integrate this derivative ## dy/dx=-y/x-siny+12xy## to get back the original function3.## ∫dy/dx dx=y ##

Folks, Differentiate implicitly \phi(x,y)=0 I get: wrt to x \phi_x+\phi_y \frac{dy}{dx} and wrt to y \phi_y+\phi_x \frac{dx}{dy} however I don't know how this is derived \phi_x dx+\phi_y dy=0

Hi Folks, It is been given that differentiation of \phi(x,y)=0 is \phi_{x} dx+ \phi_{y} dy=0 however I arrive at \phi_{x} dx/dy+ \phi_{y} dy/dx=0 via the chain rule. Where \phi_{x}=d \phi/dx etc What am I doing wrong? Thanks

Hi guys! I am trying to fit a function whose x data depends nonlinearly on the parameter of the fit and I am having hard time doing that! I will explain better: from my experiment I was able to measure my ydata e my x0 array and I know that my xdata are: x=x0+a/(1+4x^2), with a being a...

Im trying to implement the implicit Euler method in high-performance software for micromagnetic simulations, where I'm restricted to using the driving function of the ODE (Landau-Lifshitz equation) and the previous solution points. This obviously not a problem for an explicit method, since we...

I have an extremely messy system of differential equations. Can anyone offer any ideas for a general solution? p(t) is a function of t, and A is a constant.

I have an equation: r^2 = x^2 So I found out dr/dx = x/r. But when I try to find the second derivative, I get d2r/dx2 = -x^2/r^3 when the text says it should be (r^2 - x^2)/r^3. Can anyone help? My working out: r^2 - x^2 = 0 r^2 = x^2. Assume r is a function of x. rr' = x (first derivative...

Homework Statement The length ℓ, width w, and height h of a box change with time. At a certain instant the dimensions are ℓ = 4 m and w = h = 9 m, and ℓ and w are increasing at a rate of 1 m/s while his decreasing at a rate of 6 m/s. At that instant find the rates at which the following...

Homework Statement y^2 + 3x - x^3 = C, C\in\mathbb{R}\setminus\{0\} Homework EquationsThe Attempt at a Solution Keeping in mind that ##\cos ^2\alpha + \sin ^2\alpha = 1## I would go about it \left (\frac{y}{\sqrt{C}}\right )^2 + \left (\frac{\sqrt{3x-x^3}}{\sqrt{C}}\right )^2 = 1 would then...

Find the equation of the line tangent to $$\sin\left({xy}\right)=y$$ At point $$\left(\frac{\pi}{2 },1\right)$$ Answer $y=1$ I didn't know how to deal with xy. No example given

I'm under the impression that any implicit method for numerically solving ODE should be providing high stability in exchange for accuracy. I'm trying to solve the differential equation: dy/dx = -1000y + 3000 - 2000exp(-x) with intial conditions (0,0). I still can't understand how come the...

Homework Statement with answers given: Homework Equations use implicit differentiation The Attempt at a Solution I always get this answer but not the second one PLs explain the second answer for I am very desperate. Thank You

Sorry for the disturbance, So I have been looking (without success) for a way to define a variable within an implicit function in Java. What I really mean by this is I have the equation: In this function my program will give me all of the values except for px. I have tried rearranging the...

$$6x-\sqrt{2xy}+xy^3 ={y}^{2}$$ $$6-?+3x{y}^{2}{y'}^{}+{y}^{3}=2y{y'}^{}$$ Got stumped on this one answer was complicated...

How is the Implicit Function Theorem listed here (http://ocw.mit.edu/courses/mathematics/18-965-geometry-of-manifolds-fall-2004/lecture-notes/lecture4.pdf) a generalization of the usual one seen in multivariable calculus (see https://en.wikipedia.org/wiki/Implicit_function_theorem)? I've also...

I am having an issue with the declared type of the return value of a function not being recognized in its call. This function clearly has its return value declared as complex*16: !----------4-vector dot product under Minkowski metric---------- function dot4(v1,v2) result(res) implicit none...

Homework Statement I have 3 functions which define 3 constraints: A(x,y,z)=0 (nonlinear) B(y,z)=y-z=0 C(w,x,y,z)=w-(x+y+z)=0 I'm asked to calculate the partial of a function h, with respect to the variable w; with h=h(x,y,z). Homework Equations A(x,y,z)=0 (nonlinear) B(y,z)=y-z=0...

Hello there, I again have a problem with programming in Fortran 90.1. Homework Statement I would like to construct an array with an implicit do loop. I know how to get the array I want to with usual do-loop but I would like to do it without do loops. So this is the array I want to construct...

Part 1. If I want to solve the system; u-v = (h-a)e^-s w-u = (k-b)e^-t ae^s = be^t for a, b, u, in terms of the remaining variables using the implicit function theorem... If I want to know when I can solve, can I just say f(a, b, u) can not = 0? And if I set a, b, u, = 0 Than I get k and h...

Hey! :o Let $y(x)$ be defined implicitly by $G(x,y(x))=0$, where $G$ is a given two-variable function. Show that if $y(x)$ and $G$ are differentiable, then $$\frac{dy}{dx}=-\frac{\frac{\partial{G}}{\partial{x}}}{\frac{\partial{G}}{\partial{y}}} , \text{ if } \frac{\partial{G}}{\partial{y}}...

I'm having some trouble with the terminology used in calculus. My book states: "Fortunately we don't need to solve an equation for Y in terms of X in order to find the derivative of Y. Instead we can use the method of implicit differentiation. This consists of differentiating both sides of the...

I am reading several books on multivariable analysis/calculus and am trying to get a precise and rigorous theoretical understanding of implicit differentiation, including the Implicit Function Theorem ... in particular I am reading: Vector Calculus (Second Edition) by Susan Colley and...

When dealing with this separable equation for example, if I'm told to solve the given D.E. $y' = x^2/y$ so after manipulation and taking the integral I got $\frac{y^2}{2} = \frac{x^3}{3} + C$ This is the implicit form correct? Would the explicit form be $y = \sqrt{\frac{2}{3} x^3 + C}$