Differentiation Definition and 1000 Threads

maximum values for differentiation :( have a few problems with these questions, can you help :) using differentiation, find the maximum value of the following functions? 1. f(x) = -x2 + x 2. f(x) = lnx - x 3. f(x) = -x2 + 2x2 4. f(x) = x2/4 + 4/x 5. f(x) = xe-2x2 6. f(x) = sqrt(x -...

have a few problems with these questions, can you help :) 1. f(x) = -x2 + x 2. f(x) = lnx - x 3. f(x) = -x4 + 2x2 4. f(x) = x2/4 + 4/x 5. f(x) = xe-2x2 6. f(x) = sqrt(x - n)/x ; n>0 hope you guys can help !

Hai, I have the easiest problem but I am stuck at the last step, simplification. \frac{cos3x+sin3x}{cos3x-sin3x} \begin{aligned} F(x) = cos(3x)+sin(3x)\\ F'(x) = -3sin(3x)+3cos(3x) \\ G(x) = cos(3x)-sin(3x) \\ G'(x) = -3sin(3x)-3cos(3x)\end{aligned} This gives...

Hello :smile: I'm really stuck on a question and could do with some help. Homework Statement http://img268.imageshack.us/img268/2161/19947313.jpg Homework Equations http://img139.imageshack.us/img139/3478/24591171.jpg The Attempt at a Solution...

Does there exist anything like a polar complex differentiation? So there exists a gradient equation in polar coordinates something like \nabla{f} = \frac{\partial f}{\partial r} e_r + \frac{1}{r}\;\frac{\partial f}{\partial \theta} e_{\theta} But this is not for a complex number f(z) where...

I have just begun studying differentiaition and I was getting confused with how to differentiate a function of x in which x is in the base and is in the exponent as well (for example, x^2x) with respect to a=hte cahnge in 'x'. I remember my teacher telling me something about applying log...

Hello, I'm trying to prove the time differentiation property of Laplace transform. dx(t)/dt = sX(s) http://img10.imageshack.us/img10/290/tlaplace.jpg http://g.imageshack.us/img10/tlaplace.jpg/1/ how do i continue from here ?

Homework Statement Show that the set defined by the equations x + y + z + w = sin(xyzw) x - y + z + w^2 = cos(xyzw) - 1 can be described explicitly by equation of the form (z, w) = f(x, y) near the point (0,0,0,0); find the first partial derivatives of f(x,y) at the point (0,0)...

Hi I have been asked to solve the following 2 questions using 'rules' to find the derivative. (The Product Rule, The Chain Rule or The Quotient Rule.) but I can't remember what these rules are or how they are used Q1: Find the equation of the tangent to each of the following curves at the...

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...

I was working on some of my own equations and today i ended up with this differentiation thinghy, I never expected this in my equation but it just turned up :( so if there's anybody out there who loves to solve math please give this a try :) maybe its too simple :) ... i am just having doubts...

[FONT="Comic Sans MS"]Hi I'm learning laplace transform, specifically multiplying by 't' and 't^n'. Now i understand the concept that L{tf(t)} = -F'(s) but I'm confused with the differentiation part of the process (having a bit of a dim moment!). Here is the example it gives: L{sin2t} = 2...

Homework Statement Differentiate with respect to X Homework Equations 1) e^3x + ln2x 2) (5+x^2)^3/2 The Attempt at a Solution 1) isn't it just normal differentiation? so 3e^3x + 1/2x only thing i wasnt sure about was the differentiation of ln2x 2) second one i...

Homework Statement 8x^2-10xy+3y^2=26 2. The attempt at a solution (8)(2x)-(-10x)y'+(y)(-10)+(3)(2y)y'=0 16x+10x(y')-10y+6y(y')=0 y'(10x+6y)+16x-10y=0 y'(10x+6y)=10y-16x y'=(10y-16x)/(10x+6y) y'=(5y-8x)/(5x+3y) I know I'm doing something wrong but I can't see it for...

Homework Statement I am unsure how to differentiate ln(x). Homework Equations \int dx/ (x logex) The Attempt at a Solution I let u = logex So it became: \int x-1u-1dx To integrate I now need to find du/dx... which means differentiate ln(x). How does this work out?

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 By the formal definition of differentiation Prove that if f differentiable in c and f(c)\neq0 then |f| differentiable in c. The Attempt at a Solution I know that if f differentiable do it also continues but I stuck because this fact correct necessarily only for...

This is just a pretty simple "riddle" that I have always liked a lot. I didn't come up with it, I actually got it off of a website a few years ago. I'm sure for some of you, it won't be new, but here goes.. x = x x = 1 + 1 + ... + 1 (x times) x(x) = x(1 + 1 + ... + 1) x2 = x + x + ... + x...

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...

"implicit differentiation" if [x][3] * f(x) + [(f(x))][3] + f([x][3]) = 3 and f(1)= 2 find f'(1) NEED HELP REVIEW QUESTION FROM EXAM REVIEW DONT KNOW WHAT TO DO

I'm working out some problems, and I'm ending up with a term similar to the following: du/d(y/u) I'm differentiating with respect to y/u. Both y and u are variables. How can I divide that up to represent differentiation with just one variable (Even if it means expanding the term)? Is it...

Homework Statement h(sph)=exp(r2sin2(\theta)sin2(\phi)+r2cos2(\theta)) need to find gradient of this function, i have er and etheta... but can someone please tel me why when maple differentiates with respect to phi, why does it say it equals zero? coz i get...

Homework Statement Use Implicit Differentiation to find y' of the equation 5x^2+ 3xy+y^2=152. The attempt at a solution y'= (-10x-5y)/3x I would like to know if I did this right. I am not very confident in my math sometimes that why I came here. If i did this wrong will you please steer me...

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...

Homework Statement could someone please help me to answer the following problem: Suppose a wire 20 cm long is to be cut into two pieces. One piece is to be bent in the shape of an equatorial triangle and the other in the shape of a circle. How should the wire be cut so as to: a) maximize...

Homework Statement The function f(x) is defined as f(x)= -2(x+2)(x-1)^2 on the open interval (-3,3). a. Let g(x) be defined as g(x)= abs(f(x)) in the open interval (-3,3). determine the coordinate(s) of the relative maxima of g(x) in the open interval. Explain your reasoning. b. For...

Homework Statement sin(t)cos(nt) dt Homework Equations The Attempt at a Solution I tried setting u=sin(t) or cos(nt) or nt but none seems to work. Can someone give me a hint as what to set u equal to? Thanks.

Homework Statement I am asked to compute d/dt of _{c}\int^{d} ( _{a}\int^{t} f(x,y)dx)dy for t \in (a,b) for a problem involving differentiation under the integral sign. [a,b] , [c,d] are in closed intervals in \Re f a continuous real valued function on [a,b] x [c,d] Homework...

Homework Statement Find y' Homework Equations The Attempt at a Solution My solution: it's correct?

Use logarithmic differentiation to find: a.) d/dx of [(sin^-1(x^2)*sinh^-1(x^2))/(sin^4(x^2))] b.) d^2/dx^2 (sech^-1(e^(2*x))) work shown for a: let y= [(sin^-1(x^2)*sinh^-1(x^2))/(sin^4(x^2))] taking the natural logarithm of both sides: ln y= ln...

Homework Statement Find an equation of the tangent line to this curve at the point (1, -2). Homework Equations The Attempt at a Solution 2y' = 3x^2+6x y' = 3x^2+6x y'=3/2x^2+3x y+2=3(x-1) y+2=3x-3 y=3x-5

Homework Statement Homework Equations The Attempt at a Solution

Use Implicit Differentiation to find y" if xy + y - x = 1 so far i got 1y + dy/dx - dx/dx = 1/dx then i did y + y' - 1 = 0 y' = 1-y i don't understand how to get the y" . i don't think i even have y' done right!

Homework Statement A research studied the commercial fishing situation in a certain fishing zone. Denoting the total catch of corel fish in that zone in t years time from January 1, 1992 by N(t) (in thousand tonnes), he obtained the following data: t=2, N(t)=55 t=4, N(t)=98 The...

Homework Statement A vehicle tunnel company wants to raise the tunnel fees. An expert predicts that after the increase in the tunnel fees, the number of vehicles passing through the tunnel each day will drop drastically in the first week and on the t-th day after the first week, the number...

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)...

y = (sinx)2x LNy = 2xLN(sinx) + (1 over sinx)(cosx)(2x) Answer y' = (sinx)2x [2cosx over sinx + 2xcotx] and y = (cosx)cosx i did it the same way as above Answer i got was y' = (cosx)cosx [ (-sinx)(cosx) + sinx] am i anywhere right?

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...

y = (sin2x)3(x4-4x)6 divided by (cosx) + e3x i came out with an answer y' = (sin2x)3(x4-4x)6divided by (cosx) + e3x [3cot2x + 24x3-24 divided by x4-4x + Tanx + 3x could someone tell me if I am right? i don't know if this is what I am supose to do, if you want me to write out...

Homework Statement Differentiate y = \left(\frac{x+2}{\sqrt[3]{x}}\right)3 Homework Equations -Chain Rule -Quotient Rule -Power Rule -Product Rule? The Attempt at a Solution First I got rid of the fraction by taking the negative of x^3, and then used the chain rule to differentiate...

Homework Statement Prove that \frac{dy}{dx}=\frac{y}{x} for \sqrt{\frac{x}{y}}+\sqrt{\frac{y}{x}}=10 x is not equal to y which is not equal to 0 The Attempt at a Solution Tried all the normal methods but none seem to work...anyone have any ideas?

Homework Statement The curve y = ax^{2} + bx passes through the point (2,4) with gradient 8. Find a and b . I have no idea how to work out a and b , do I use simultaneous equations? Homework Equations The Attempt at a Solution I have no idea how to work out a and b , do I use simultaneous...

Homework Statement Find derivative of y with respect to x. Sin(xy) = Sinx Siny Homework Equations The Attempt at a Solution Use chain rule (product rule for inner function) to differentiate the left. Use product rule to differentiate the right and I get the following...

Homework Statement I am trying to differentiate log((x+(x^2+y^2)^0.5)/(-x+(x^2+y^2)^0.5)) with respect to y Homework Equations I know that d/dx of ln(x) = 1/x but i am getting really confused when it comes to differentiating wrt to y? Can I have some help please! The Attempt at a...

1. Homework Statement , attempt at a solution Please see attached. I'm actually busy with a physics problem, but solving it requires that I complete this part correctly. It's straightforward differentiation, but I think I made an error with my signs somewhere and I can't for the life of me...

Homework Statement In polar coords: y = rsin(\theta) y' = dy/dt = r'sin(\theta) + rcos(\theta) \theta' If I want \partial r' / \partial y' can I just solve for r' and take the derivative of y'? so \partial r' / \partial y' = 1 / sin \theta I am hoping this is incorrect because...

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 differentiate y = (3x2-4)1/2+(x2+4)1/2 with respect to x Homework Equations y = (3x2-4)1/2+(x2+4)1/2 The Attempt at a Solution dy/dx = (3x2-4)1/2dy/dx+(x2+4)1/2dy/dx Is it correct...? for the first part let u = (3x2-4)1/2 du/dx = 6x y = u1/2 dy/du = 1/2u-1/2 dy/dx =...