Derivatives Definition and 1000 Threads

For example, if I want to show that there is no real # solution to x2 + 24x2 = -1 is it correct to show that d2/dx2( x4 + 24x2 ) = d2/dx2(-1) ---> 12x2+48 = 0 And since x^2 is >0 or =0, 12x2+48 ---> 0 + 48 \neq 0 Therefore, there is no real number solution to x2 + 24x2 = -1...

Homework Statement find the dy/dx of y = Sin4 x2 - Cos4 x2 Homework Equations derivatives and identities factoring dy/dx (Sinx) = Cosx dy/dx (Cosx) = -Sinx The Attempt at a Solution y = (Sin2 x2 - Cos2 x2) (Sin2 x2 + Cos2 x2) im stuck at this part i don't know how to...

Homework Statement y=(sin2x)(cos2) Homework Equations Product Rule for Derivatives identities: derivatives of Sinx = Cosx Cox = -Sinx The Attempt at a Solution i used the product and chain rule for derivatives then do the identities y = sin2x*cos2x dy/dx = (Cos2x)(2)...

Homework Statement A straight line is drawn from the point (0,a) to horizontal axis, and then back to (1,b). Prove that the total length is shortest when the angles \alpha and \beta are the same. 2. Homework Equations /graphs [PLAIN]http://dl.dropbox.com/u/23215/Graph.jpg The...

Homework Statement Show that the expression A, T(dP/dT)|V - P is equal to expression B, T^2 * [d(P/T)/dT]|V Also, show that expression C, -[d(P/T)/d(1/T)]|V is also equal to expression B Homework Equations A: temperature * (dPresure/dTemperature at constant volume) -...

Homework Statement is the derivativethe same thing as the slope of the function for which we're finding the derivative? Homework Equations The Attempt at a Solution

Homework Statement Find y'' if y=1/3(1+cos^2(√x)) Homework Equations The Attempt at a Solution Now I believe I got the first derivative right since the teacher marked ir right, but my real question here is what do I do with the 1/3? Is it ok to throw away the constant when I...

Homework Statement find the largest distance and shortest distance from the origin to the conic whose equation is 6x2 + 4xy +3y2 - 28=0 and hence determine the lengths of the semi axes of this conic Homework Equations Lagrange identity F= f + λφ = 0 distance = d2 =x2+ y2+...

Homework Statement Find the absolute maximum and minimum values of f on the set D. f(x,y) = 1+4x-5y D is the closed triangular region with vertices (0,0) (2,0) (0,3) Homework Equations To find the absolute maximum and minimum values of a continuous function on a closed, bounded set : 1. Find...

Homework Statement Show that there is a polynomial function f of degree n such that: 1. f('x) = 0 for precisely n-1 numbers x 2. f'(x) = 0 for no x, if n is odd 3. f'(x) = 0 for exactly one x, if n is even 4. f'(x) = 0 for exactly k numbers, if n-k is odd Homework Equations The...

Hi, I have a coupled system of ODE like: w1'' = A w2'' + B w1 + C w2 w2'' = D w1'' + E w1 + F w2 I need to solve it analytically but it seems it cannot be solved using eigenvalue method. My concern is first that if this system have sufficient equations and if so how it can be solved...

Ok, I just had a lecture recently the attached picture is what it was about. I understand it all, however at the end it says we havnt proven it yet - just wondering how DO you prove it then? Thanks, Owen

Homework Statement I have no homework problem to ask, but rather a general question. Ill give and example of a potential function V = 3x^2 + 2y^2 i know to find Fx i have to differentiate 3x^2 with respect to x and 2y^2 with respect to y. But i have seen cases where someone takes the...

Homework Statement Show, with appropriate examples, that the conditions g(x) < f(x) < h(x) and derivative(g(x0))=derivative(h(x0)) = m does not imply derivative(f(x0)) = m or even exists. And with some additional condition. Homework Equations derivative g(x) = lim(h tends to zero)...

What exactly does it mean for a function to have continuous partial derivatives? How do we see this?

Hi, I am in calculus and am having major struggles. If someone could provide a walk through on how to answer these questions, that would be fantastic. Cheers! Let f(x)=−3x+6 if x<-3 = 15 if x > -3 Find the average rate of change of f(x) on the interval −5<x<5 . The average rate of...

Homework Statement calculate the derivative of the following functions? f(x,y,z,t) = (x-1)(2-y)z + (t^3 - 1)xyz g(x,y) = 1/(1 + exp(-(ax + by + c)) h(x,y,z) = (x-1)^2 exp(x) + (y-2)^3 * z^3 The Attempt at a Solution the way i was thinking was may be split the problem into...

Hi there. Well, I wanted to know how to find the second derivatives of a function using implicit differentiation. Is it possible? I think it is. I think I must use the chain rule somehow, but I don't know how... I'm in multivariable calculus since the function I'm going to use could be seen as a...

I need help with this one: Find fxy in: ln(x+y)/(xy) .. the ln applies to the whole problem.

Questions in derivatives I want to check my answer http://store1.up-00.com/Oct10/KpR43940.jpg

I want check my answer in derivatives (part 2) http://store1.up-00.com/Oct10/7uV34128.jpg

I want check my answer in derivatives (part 1) http://store1.up-00.com/Oct10/p0O34128.jpg

Homework Statement proving the nth derivative of x to the n power is n factorial Homework Equations The Attempt at a Solution proving it for n=1 d^(1)x^1/dx = 1!=1 (a) d/dx x^1 =1 (b) a=b therefore at n=1 it is true supposing it is true for n=k then d^(k)x^k/dx = k...

Homework Statement The problem is : take the derivative of (x - a) Homework Equations Power Rule : f '(x) = r x^(r-1) Difference Rule : f '(x) = g '(x) - h '(x) The Attempt at a Solution This is such a simple problem but I don't understand how my solutions manual and Wolfram...

I'm having issue with one problem. We're asked to break down the problem into partial fractions to solve for the integral. Well, I'm stuck on one. I'm being asked for the values of A, B, and C for the following problem. ∫((9x^2+13x-83)/((x-3)(x^2 + 16)))dx I can get it worked down...

Homework Statement The function given to me is F(x) = A + Bx. x is the displacement, F(x) is the force as a function of that displacement, and A and B are constants. From the function, I'm supposed to find the velocity of the function as a function of x. We also know that the items...

Homework Statement f(x) = 10(sin(x))^x ----> find f '(1) The Attempt at a Solution I have tried several different approaches, but still get stuck with a wrong answer every time f(x) = 10(sin(x))^x let f(x) = y so y=10(sin(x))^x then ln y = ln10(sin(x))^x...

I have a question about these two. I have a direction derivative at a in the direction of u defined as: f'(a;u) = lim [t -> 0] (1/t)[f(a + tu) - f(a)] And the partial derivative to be defined as the directional derivative in the direction of u = e_i. My text, Analysis on Manifolds by...

Homework Statement find the equation on the tangent plane of yz=ln(x+z) at point (0, 0, 1 ) Homework Equations Tangent plane equation... The Attempt at a Solution I wasn't sure how to determine the partials on this equation. My attempt was to rearange as ln(x+z)-yz=0 so Fx =...

Homework Statement the total surface area of a right circular cylinder is given by the formula: (A = 2Pir(r + h) ). where r is the radius and h is the height. sub part a) find the rate of change of A with respect to h is r remains constant i know how to take derivatives. the only...

Let \bar{z} = x+iy. We are given that x = \frac{z+\bar{z}}{2} & y = \frac{z-\bar{z}}{2i}. We are trying to derive \partial F/\partial\bar{z} = 1/2(\partial F/ \partial x + i \partial F/ \partial y), where F(x,y) is some function of two real variables. Using the chain rule I get \partial...

Homework Statement Calculate the following, expressing all results with uncertainties both in absolute and relative (percentage) form: a) A + B b) A x B c) Asin(theta) d) A^2 / Bcos(theta) The relevant formula for the absolute uncertainty is below, but i have no idea how to...

ey guys Generally i just do these without thinking, however i was checking some work today with a friend and he is adament i did my derivative wrong... If i can double check with you Well firstly 'c' is simply a constant q1 and q2 are generalised coordinates IZG1 is simply the...

I am currently learning calculus and just had my lecture on the chain rule. I noticed that we haven't learned how to take the derivative of a function like 2^2+x or 3^4+x. Any example works.. Is this something I will learn later as I progress through calculus or what?

Homework Statement f(x,y)=2Sin x Cos y g(x,y) = 2Cos x Sin y verify that d(fg)/dx = g(x,y) df/dx + f(x,y) dg/dx The Attempt at a Solution first of all I worked out the partials derivatives in respective to x and y, for both functions df/dx = 2Cos x (but I've a gut feeling that it...

f(x,y)= xy2/(x2+y2) if (x,y)\neq(0,0) =0 if (x,y)=(0,0) Show that the partial derivatives of x and y exist at (0,0). This may be a really stupid question, but would the partial derivatives of x and y at (0,0) just be 0? I tried taking that partial derivatives of xy2/(x2+y2) and...

My professor did this in lecture, and I can't figure out his logic. Can someone fill in the gaps? He went from: dS = \left( \frac{\partial S}{\partial P} \right)_T dP + \left( \frac{\partial S}{\partial T} \right)_P dT (which I totally understand; it just follows from the fact that...

Homework Statement http://webwork2.asu.edu/webwork2_files/tmp/equations/9f/ab106661843d52ded597f9bcb68ace1.png find f'(x) Homework Equations The Attempt at a Solution I tried 8x^.5(-4), 0, and a few others once my original try came up with nothing. I realize sqrtx should come...

f(x, y, z) = xe^y + ye^z + ze^x, at (0, 0, 0), directional vector v = <-2, 0, 5> i solved for gradient f = (e^y + ze^x, xe^y + e^z, ye^z + e^x), at f(0,0,0) to be... gradient f = (1,1,1) this would make the answer just be -2 + 0 + 5 = 3 but this isn't right. can someone show me...

1. Find the derivatives of the spherical coordinates in terms of df/dx, df/dy, and df/dz. 2. f(x,y,z) x=rcos\thetasin\varphi y=rsin\varthetacos\varphi z=rcos\varphi 3. The Attempt at a Solution [/b] I took the derivatives of the three equations and I got...

Suppose that f:\mathbb{R} \to \mathbb{R} is continuous and f'(x_0) exists for some x_0 . Does it follow that f' exists for all x such that |x-x_0|<r for some r>0 ?

Homework Statement Basically I have two problems that are asking for the partial derivative with respect to x and y at a certain point on a level curve graph, and a contour map. How do you go about doing these? There is no function given, so I don't really know what they expect you to do...

Homework Statement (-1)^4*xdx + (8y-y^2-13)dy=0; y(0)=4; 1. Use dsolve to obtain a solution. 2. As dsolve was not much help find an implicit solution of the form f(x, y) = 4 Homework Equations --- The Attempt at a Solution the dsolve part was easy, i just did: syms x y t...

Homework Statement Hi there. Well, I've got some doubts on the partial derivatives for the next function: f(x,y)=sg\{(y-x^2)(y-2x^2)\} Where sg is the sign function. So, what I got is: f(x,y)=f(x)=\begin{Bmatrix}{ 1}&\mbox{ if }& (y-x^2)(y-2x^2)>0\\0 & \mbox{if}& (y-x^2)(y-2x^2)=0\\-1 &...

Homework Statement Hi there. Well, I got the next function, and I'm trying to work with it. I wanted to know if this is right, I think it isn't, so I wanted your opinion on this which is always helpful. f(x,y)=\begin{Bmatrix} (x+y)^2\sin(\displaystyle\frac{\pi}{x+y}) & \mbox{ si }&...

Is there a simple way to show that when we differentiate the following expression (call this equation 1): Y(x) = \frac{1}{n!} \int_0^x (x-t)^n f(t)dt that we will get the following expression (call this equation 2): Y'(x) = \frac{1}{(n-1)!}\int_0^x (x-t)^{n-1}f(t)dt It's simple...

Find f ' (2) given the following. g(2) = 3 , g ' (2) = -2 h(2) = -1 , h ' (2) = 4 a. f(x) = 2g(x) + h(x) b. f(x) = g(x) / h(x) c. f(x) = 4 - h(x) d. f(x) = g(x)*h(x)

Homework Statement Question #2 http://img830.imageshack.us/img830/8185/0000825.jpg Homework Equations The Attempt at a Solution I can of course find the derivatives for both functions. When I set them equal to each other I get x=1/2 that's where the functions have parallel tangent lines for...

I'm having trouble understanding why a derivative of a time dependent vector function is orthogonal to the original function. Can anybody give me some enlightenment? I searched around for some previous talk about this, and I can't find anything. Thanks.

Reading Roger Penrose's The Road to Reality, I wondered what is the relationship/difference between these? Can one be expressed simply in terms of the other? The exterior derivative seems to be only defined for form fields. He says the covariant derivative of a scalar field (0-form field) is the...