Differentiating Definition and 262 Threads

Homework Statement z = cr^2 Homework Equations The Attempt at a Solution I have a pretty simple question. What is the second derivative of the z equation. I know that z' = 2crr'. Am I correct to say that z'' = 2cr'^2 or is it something else? Hopefully my question...

Homework Statement I need to differentiate uxe^-x in order to do a reduction order question. Homework Equations d/dxf(x)g(x) = f(x)g'(x) + g(x)f'(x) <--- that's the product rule about 2 variable The Attempt at a Solution I would assume y' = -uxe^-x + u'xe^-x I was told...

Hi So this is pretty basic but how would you differentiate u = (a^2 + b^2 + c^2) please where a, b and c are three separate, independent variables. Please. would it be (2a+b^2+c^2)+(2b+a^2=c^2)+(2c+a^2+b^2)? Thanks

Hi so I am new to calculus and need help with differentiation The question is: Differentiate the following function: sqrt(x^2-8x+20) So far I have gotten =(x^2-8x+20)^(1/2) =(1/2)(x^2-8x+20)^(-1/2) * 2x-8 I am unsure where to go from here I know we are supposed to use the chain...

Homework Statement integral 0 to infinite (x^3)(e^-8)(cos(5x)) dx Homework Equations integral by part? The Attempt at a Solution should I use integral by part?

I was reading on a textbook and came across a step and I had no idea how the author got the next step from it. This was basically differentiation of a definite integral. So here it is. \frac{\partial}{\partial t}{\int_0^t}{\int_0^1}u_t^2(x,s)dx ds So I figured that u_t=\frac{\partial...

If you differentiate the formula for the volume of a solid sphere, 4/3 \pir3, you get 4\pir2, the formula for the surface area. This seems to make sense, as, onion-like, the sphere is made up of successive surface areas, so the rate of change will be the surface area for any given r. If you...

Homework Statement \int_{2}^{y(x)}e^{t^2+1}dt + \int_{x^2+3x}^{0}\frac{e^z}{1+z}=0 I need so find y'(0). The Attempt at a Solution \frac{d}{dx}\int_{2}^{y(x)}e^{t^2+1}dt =y'(x) \cdot e^{y(x)^2+1} \frac{d}{dx}\int_{x^2+3x}^{0}\frac{e^z}{1+z}=-\frac{e^{x^2+3x}}{x^2+3x+1}\cdot...

Homework Statement For the function y= |x2-4x+3| a. Sketch the function b. Is the function continuous? Explain. c. Is the function differentiable everywhere? explain d. find gradient of curve at the point where x = 3/2 Homework Equations chain rule, differentiating... The...

Hi, First: Hello, Physics Forums (this is my first post)! Now to business. I am trying to enter the Distance Forumula: m = sqrt([x2-x1] + [x2-x1]) into the Equation Solver on the HP-50g. However, I cannot find a way to subscript variables. Of course, I could just enter, m= sqrt ([A2-B1] +...

how to differentiate the following with respect to x x:cos2x thanks for ur help, sorry that i couldn't write it in a fraction form

Ok so i was wondering if what i am doing is correct, But it gets the wrong minimum point? So my function is y=|x+4| 1) y^2=x+4 2)2y(dy/dx)=1 3)dy/dx = 1/2y 4)dy/dx = 1/2|x+4| I set that 0 and get 0=1/(2(|x+4|)) Am i write in thinking this cannot be solved? or missing something...

okay we know that velocity is in meters per second and that acceleration is in m/(s^2) , so if I take the derivative of velocity with respect to time i get acceleration . but just looking at the units , if i start with velocity m/s (ms^-1) this might sound crazy but can i just take...

Homework Statement Differentiate the following: y = e4x/x2+1 2. The attempt at a solution I know you have to use quotient rule here. so I wrote out (x2+1)* d/dx e4x) - d/dx (x2+1)* e4x all over (x2 + 1) 2 I have no idea how to continue on from here...how would you...

Homework Statement Find dy/dx, given y = sin( 3 x ) cos( 6 x ) Homework Equations product rule= f'g+g'f The Attempt at a Solution I used the product rule and got this, but its supposedly wrong, what have i done wrong?((3*cos(x))*(6*cos(x)))+((6*sin(-x))*(3*sin(x)))

1. Differentiate cosh(x) using first principles 2. cosh(x) = (e^x+e^-x)/2 From previous exercises, I know the answer will be sinh(x)= (e^x-e^-x)/2 but I cannot get to the answer. I seem to be left with the equation: lim h ---> 0 (e^2x*e^2h +1-e^h*2e^x +e^h)/(2h*e^x*e^h) But when...

Homework Statement Given: f is integrable on [a,b] and has a jump discontinuity at c in (a,b) (meaning that both one-sided limits exist as x approaches c from the right and from the left but that Lim(x->c-)[f] is not equal to Lim(x->c+)[f]). Show that F(x) = Integrate[f,{a,x}] is not...

Again, I'm not sure whether this is the best place to post this question but its to do with gauge transformations, etc. The question itself is rather stupid... If we have a matrix U(g) (a Lie Group) and a vector φ in C (which is a scalar in spacetime) - does it make sense to use the chain...

Hello, First of all, I am not trying to "spam" subforums. I found out that my thread shouldn't be posted under homework. Anyways, here it is. Integration Let say there's a polynomial, 5x+6 and you want to integrate from 0 to 3 respect to x, how do you input in MATLAB? (I guess you can't...

Hi, I need to differentiate the following \frac{d}{dx}[e^{-2x}y] Does the `dx` mean that the y turns into x? I know i have to use the product rule.

Homework Statement we have been doing some error analysis in school, but they were very straight forward for example. centripetal acceleration : Fc = 4pi^2 m R / T^2 however, for my project i must find the uncertainty in the angle that i measured. the angle is formed by a cardboard...

Homework Statement we have been doing some error analysis in school, but they were very straight forward for example. Centripetal Acceleration : Fc = 4pi^2 m R / T^2 however, for my project i must find the uncertainty in the angle that i measured. the angle is formed by a cardboard...

i am having trouble differentating this function with respect to y c= 425 + 1.2ln(y/(y+2)

Homework Statement Don't really know what to do with this one, any help welcome If A, B and α are constants, independent of x, and y= Acosαx + Bsinαx Evaluate the derivates y'=dy/dx y^n=d^2y/dx^2 Determine values of A, B and α such that y satisfies y^n+y=0 and y(0)=0, y'(0)=1...

Homework Statement Say f(z) = Σ(z^n), with sum from 0 to infinity Then we can say f'(z) = Σn(z^n-1), with sum from 0 to infinity (i) = Σn(z^n-1), with sum from 1 to infinity (as the zero-th term is 0)...

Optimization problem -- Trouble differentiating function Homework Statement The efficiency of a screw, E, is given by E=\frac{(\Theta - \mu\Theta^{2})}{\mu + \Theta} , \Theta > 0 where \Theta is the angle of pitch of the thread and \mu is the coefficient of friction of the material, a...

Homework Statement Homework Statement [/b] Hello. I'm trying to solve a non-linear problem and I have been working through the notes on this pdf to try and understand the method before I use it but I get stuck at one of the steps. The pdf is here: http://www.nrbook.com/a/bookfpdf/f9-7.pdf I...

Homework Statement Consider I = \int^{1}_{0} \frac{t-1}{ln t} (No, the problem does not contain a dt at the end of the integral, but I'll assume its a typo) Think of the t in t-1 as the a=1 limit of t^a. Let I(a) be the corresponding integral. Take the a derivative of both sides...

Hey everyone, I'm new to using the Maxima software and I'm having some trouble. When I enter the following formula to be evaluated: diff(1-exp^(-t/R*C),t); I get the following output: \frac{log\left( exp\right) \,C}{{exp}^{\frac{t\,C}{R}}\,R} This doesn't look right, even if I...

Hello. I have the following query. Consider a continuous function f(x). We want to know whether this function ever gets zero or not. So we make the assumption that it does. If (e.g) we have f(x)=x^2 + 4x + 2 - cosx we'll assume that f(x)=0 (=) x^2 + 4x + 2 -cosx =0 now we differentiate with...

a particle moves along the curve xy=10, x=2 and dy/dt=3, what is the value of dx/dt? i tried product rule and got x*y*dy/dt + y*x*dx/dt = 0 and the answer that i get doesn't appear on the multiple choice answers a)-5/2 b)-6/5 c) 0 d) 4/5 e) 6/5 i don't know what I am...

Homework Statement L(t)=15(0.5^(t/26)) Find the rate of L, when t=60 Homework Equations The Attempt at a Solution L'(t) = (15/26)(1/2)^(t/26)ln(1/2) L'(60)=(15/26)(1/2)^(60/26)ln(1/2) = -0.08 Did I do this right? If I did it wrong, please say where, I am having great...

Hey all, I'm really having a hard time figuring out a couple of problems in which I have to differentiate: 1: \frac{e^3^x}{\ln x} I just don't know how to put it together... I know that e^3^x is 3e^3^x, and I know that you can't different \ln x, so I don't know what to do from there...

Homework Statement Differentiate sin x - 1/3 sin^3 (x) + 7 The attempt at a solution sin x becomes cos x, and 7 becomes 0. Using the product rule on (1/3) sin^3 (x) + 7 I get: (0) sin^3 x + (1/3) [derivative of sin^3 (x)] Getting the derivative of sin^3(x) is the tricky part I'm...

Homework Statement does anyone know how i can differentiate a strong acid from a weak acid and likewise for a strong base and a weak base based on its chemical formula? Homework Equations The Attempt at a Solution

Homework Statement Hi all. I have a time-dependent variable called x. I wish to differentiate x2 with respect to the time t, and this is what I have done: \frac{d}{dt}x^2 = \frac{d}{dx}x^2\frac{dx}{dt} = \frac{d}{dx}x^2\dot x. where the dot over x denotes differentiation with...

Homework Statement \int\sqrt{49-4x^2} I have done the integration to the best of my ability. My teacher requires that I differentiate the answer to get back to the original integrand. Can someone please check my work and help me along with the differentiation? Homework Equations U...

Why does the derivative of (sin(x* theta))/(2x-1) equal [(-2sin(x*theta))/(2x-1)^2]? I'm an undergraduate physics student with a shaky math background, who's enrolled in an advanced Physics math class for which I lack prerequisites. I'm working an infinite series where the general term comes...

Homework Statement d/dx (\int^{x}_{0} x2t2dt) So the problem is to solve the derivative of the integral \int x2t2dt from 0 to x. Homework Equations d/dx (\int^{x}_{a} f(t)dt) = f(x) The Attempt at a Solution I'm really unsure of how this should be computed but this was my guess...

Homework Statement Differentiate the identity sin2x = 2sinxcosx to develop the identity for cos2x, in terms on sin x and cos x Homework Equations The Attempt at a Solution Im not sure where to start with this one. Should I find the derivative of both sides of the equation, and...

Hey guys, I've just recently started calculus, and just trying to get to grips with it. I'll use an example for my question; if y=e^x, then the source suggests rearranging to \ln y=x, the differentiating with respect to x yields \frac{\delta}{\delta{x}} (ln\ y)=1. I understand that for my...

How would I go about finding the derivative of x2 + y2 = 36. I know it is a circle with radius 6. Is there a better way to find the derivative then: y2 = 36 - x2 y = (36 - x2)1/2 y = 1/2(36 - x2)-1/2(-2x) y' = -x/(36-x2)1/2

Struggling with these two questions, any ideas? A Homework Statement Differentiate with respect to x sin-1 2x - 4 cos-1\frac{x}{2} Homework Equations The equations I have in my notes are identical to those derived here...

Homework Statement I'm having trouble factoring this to its simplest term. I'm not very good at factoring, but I'm working on it. I was hoping that someone might be able to help me here. Homework Equations Find the critical points for f(t) = t * sqrt(4 -(t^2)) on the closed interval [1...

The problem: Find the value of dz/dx at the point (1,1,1) if the equation xy+z3x-2yz=0 defines z as a function of the two independent variables x and y and the partial derivative exists. I don't know how to approach the z3x part. I thought you would use the product rule and get 3(dz/dx)2x +...

Not really a homework problem... just a general question (this seemed like the place to put it...). Say I have three functions: f,g,h:\mathbb{R}^2\rightarrow\mathbb{R}^3 and an expression along the lines of: \left\langle f(u_1,u_2),g(u_1,u_2)\right\rangle h(u_1,u_2) What...

Homework Statement X / 1+sinX The Attempt at a Solution Quotient rule (1+sinX)(1)-X(1+cosX) / (1+sinX)2 To: 1+sinX-X-XcosX / (1+sinX)2 But when I look at the answer in the back of the book, it's wrong.

Hi. I believe this may have been addressed previously but I wanted to make sure since I don't think it was completed. Hi I know that differentiating sin = cos , and differentiating cos = -sin. Time to prove it. [SIZE="4"]Q3: Prove that: \frac{d}{{dz}}\sin z = \cos z We know the...

Hello, in coming up with a general form for finding the derivative of a product there is one step I do not understand. if we let u, v and y be functions of x then: dy/dx = u(dy/dx) + v(du/dx) + du (dv/dx) From there we take the lim as dx -> 0 of each term and the textbook I am...

Given two arbitrary qubits, is there a test I can do that will always tell orthogonal qubits apart (but may fail if they are not)? Does it necessarily destroy the qubits' states?