Differentiating Definition and 262 Threads

Differentiate $x^{1/2}\left[c_1J_{1/4}(x^2/2)+c_2J_{-1/4}(x^2/2)\right]$.

Homework Statement Prove that d/dt[r.(vxa)] = r.(vxda/dt) Homework Equations r, v, a are position, velocity and acceleration vectors. ..r.(v.. is the dot product. ..vxa.. is the cross product The Attempt at a Solution I expand the equation using the product rule for dot and...

Homework Statement Differentiate twice: z = sinx Homework Equations Product rule Chain rule The Attempt at a Solution dy/dx = dy/dz * dz/dx dy/dx = dy/dz * cosx Using the product rule: d^2y/dx^2 = d^2y/dz^2 * cosx - dy/dz * sinx According to the answer in the book...

Quick question on typical integration/differentiation. What is the justification for differentiating some integrals with respect to constants in order to obtain results for them, i.e. \frac{∂}{∂α}\int e^{-αx^{2}}dx=\int-x^{2}e^{-αx^{2}}dx? It seems to me α is a constant, so it seems a little...

Homework Statement The Attempt at a Solution When the textbook says: Differentiating both sides of x^3 + y^3 = 6xy with respect to x, regarding y as a function of x, and using the Chain Rule on the y^3 term and the Product Rule on the 6xy term, we get I really don't get what...

Homework Statement 1. a) A rope 25m long is cut into two pieces. One piece is bent into the shape of a square, and the other into the shape of a circle. How should the rope be cut to maximise the total area enclosed by the pieces? And how should it be cut in order to minimise the total...

Even though I've taken 3 semesters of calc, some of the terms are used interchangeably and are a bit obfuscated (at least in my mind lol). I understand how to take the derivative of a function with respect to 1 or more variables, but I'm reading Mary L Boas Math methods in physical science and...

Homework Statement Verify the identity: arctanx + arctan(1/x)=∏/2 using calculus theory. (Hint: Differentiate the left hand side of the identity) Homework Equations ? The Attempt at a Solution is this correct? tan(arctanx + arctan(1/x)) = [tan(arctan(x)) +...

Hi, I found on youtube a video showing the steps to differentiate tan(x). I can follow the steps quiet easily but I'm not sure which rule is being used when substituting u for cos(x) and du for sin(x)dx. So which rule is being used and how do I know which is u and which is du. Thanks

Homework Statement Given here is an Operational Amplifier, its feeding Voltages are +-10. A) Calculate Vin to get a Vout of -2V, point out the direction of the current in this case (From a to b or b to a) http://img72.imageshack.us/img72/2550/needheed.jpg The Attempt at a Solution...

k guys.. i'd like to try to figure out how to get to the derrivatives on my own so really just looking for a right or wrong. 1. f(x) = e^(3x^2+x) find f'(2) f'(x) = e^(3x^2+x) * (6x+1) f'(2)= e^(3(2)^2+2) * [6(2)+1] f'(2)=13e^14 ... correct?2) find slope...

1. my function is: f(x)=log 1.5 (-.76x+305). f(x)= log base 1.5 of -.76x+305 3. How do i differentiate it? here is what i have so far: (1/((-.76x+305)ln1.5))*(-.76/dx)

Homework Statement A funny car accelerates from rest through a measured track distance in time T with the engine operating at a constant power P. If the track crew can increase the engine power by a differential amount dP, what is the change in the time required for the run? (Use any variable...

find the derivatives of differentiation of trigonometric functions 1. y=cos(3x^2+8x-2) 2. y=tan^3 2x 3. y=sin5x sin^5 x 4. y=Square root of 4sin^2x+9cos^2x help here please.. i can't understand trigonometric functions sorry admin or moderator, i just search the net on how...

Homework Statement if y = K sin(Gx + 5) what is dy/dx Homework Equations y=sin x dy/dx = cos x The Attempt at a Solution y = K sin(Gx + 5) dy/dx = KG cos (Gx +5) (1) or dy/dx = KG cos GX + 5 (2) i think it is (1) is this correct or it is non of these...

Hey everybody! Physicists have no problem differentiating a function of many variables - in flat space R^n. But I don't like how many books don't give examples of how this done in a manifold- even if it may be easy when one finally understands it. For example, how do I differentiate a...

Hi there, I should probably know this (attempting to do a PhD in physics!) but is there a way to differentiate between longitudinal and shear acoustic waves in a solid? I know that seismologists know which is which by using the time of flight difference for the two types of waves and the...

Homework Statement Differentiate, f(x)=71+x/1-x Homework Equations The Attempt at a Solution Working this out, hoping it's right as I was going along, my final answer is 71+x/1-x * (2ln7)/1-x

Homework Statement I'm doing a optimisation question and I get to a point where I have to verify a maximum using a double derivative and I need to differentiate -5sin^2(x) Homework Equations -5sin^2(x) The Attempt at a Solution -10cos(x)sin(x) I am not sure if the answer is positive...

differentiating for "y" Homework Statement I don't quite understand the reason why one can \frac{d}{dx} y2 and get 2y \frac{dy}{dx} when using implicit differentiation. Why can one even go as far as to change y2 to 2y? Homework Equations The Attempt at a Solution I see the chain rule is...

Differentiate the following: u = 2 (x-t2 / 3)et/3 Here is my attempt I have to find du/dx and du/dt du/dx = 2 (x-t2 / 3)et/3 du/dt = -4t/9 (x-t2 / 3)et/3

Homework Statement Differentiate the following function: f(x) = x\sqrt{x^{3}+2x} Homework Equations N/A The Attempt at a Solution Here's my attempt: First I rewrite it as: f(x) = x(x^{3}+2x)^{\frac{1}{2}} Now, I differentiate using chain rule: f(x) =...

Homework Statement Does this look correct? How do I know when to stop simplifying things? Sometimes it comes out to a nice little expression, and other times it's a long solution. In the latter, I spend too much time trying to simplify it further! Homework Equations The Attempt at a...

Homework Statement Calculate the integral I = \int (t^x - 1)/ln(t) dt, boundaries: 0 \leq t \leq 1, x \geq 0 by differentiating first with respect to x. Homework Equations - The Attempt at a Solution I have no idea how to solve this, but it's on our sample exam and there are no...

Homework Statement By differentiating the summation, show that ∂/∂b₀ ƒ(b₀ , b₁) = -2 ∑_(i=1)^n (y₁ - b₀ - b₁x₁) Homework Equations the ‘derivative of the sums’ equals ‘the sum of the derivatives’: The Attempt at a Solution How would we partially differentiate a summation...

What is the difference between the float and fly and move freely in space first, and within the Earth's atmosphere?

Find the general solution to: dy/dx = ex+y Im not sure if I am doing this right or not. i tried saying ex+y = ex x ey and using partial differentiation to solve it but keep getting the same as the question: ex+y i know differentiating ex gives ex so is it the same in this case?

Hello!I'm getting confused when differentiating summations. I understand that if you differentiate an expression and it gives a kroneker delta, that then sums over the appropriate summation and it disappears. But in my notes it has \frac{\partial}{\partial p_{i}} [-k \sum_{i=1}^{r} p_{i} ln...

Hello! I am very VERY confused! Would anyone please be kind enough to point me in the right direction. I read that, in general, the derivative of a tensor is not a tensor. What do you find when you differentiate a tensor, then? I thought that you wanted to find the acceleration, to...

I am not sure whether there is any difference between differentiating complex and real numbers... I am just trying to differentiate: e^(2+3i)x = (2+3i)e^(2+3i)x Is this correct? I have a feeling its not this simple.

If r and s are vectors that depend on time, prove that the product rule for differentiating products applies to r.s, that is that: d/dt (r.s) = r. ds/dt + dr/dt .s -- I'm not entirely sure how I'm supposed to go about proving this, can anyone point me in the right direction, please...

Homework Statement How would you differentiate, (v^3-2v*squareroot v)? Homework Equations The Attempt at a Solution would it look like...3v^2 - v^-1/2 ?

Homework Statement y = -5x3 + 4/x5 + 1.7pi Homework Equations Differentiate each Function. Derivatives The Attempt at a Solution I have done question like these before but this is the first time using pi. I used all derivative rules none of them give me the right answer. The answer I am...

Homework Statement Differentiate. y=x^2 + 4x +3/(square root x) and H(x)=(x+x^-1)^3 Homework Equations The Attempt at a Solution For the first one I got x^3/2 + 4x^1/2 + 3x^-1/2 But I don't know if that is correct or where to go from here? The second I really...

Hey All, Here's a stupid and probably ridiculously easy question, but I want to make sure that I have it right. Let G be a Lie group with Lie algebra \mathfrak g . Assume that H \in \mathfrak g and \phi \in \mathfrak g^* the algebraic dual. Assume that X(t) is an integral curve...

Homework Statement d/dx(E^xy+y) Homework Equations The Attempt at a Solution How do you differentiate this phrase

Homework Statement Differentiate the following functions with respect to x. a) \int (t2 + cos(t7))/(1 + t4) dt [0, x] b) \int (t2 + cos(t7))/(1 + t4) dt [2, x] c) \int (t2 + cos(t7))/(1 + t4) dt [0, sin x] d) \int (t2 + cos(t7))/(1 + t4) dt [x, sin x] e) \int (x2 + cos(t7))/(1...

Basic question on scalar filed theory that is getting on my nerves. Say that we have the langrangian density of the free scalar (not hermitian i.e. "complex") field L=-1/2 (\partial_{\mu} \phi \partial^{\mu} \phi^* + m^2 \phi \phi^*) Thus the equations of motion are (\partial_{\mu}...

I think I know how to do this but I'm completely blank at the moment. Do I differentiate 'ln' and then differentiate 2^x and 3^x in the denominator?

Homework Statement I am working on a problem that asks to use the integral form of the continuity equation (for a steady flow) and show that it can equal this (by taking the derivative of it): dr/r + dV/V + dA/A = 0 where V is Velocity and r is the density. Homework Equations What would...

My question is just a concept that I don't understand. When differentiating a power series that starts at n=0 we bump that bound up to n=1. My question is do we always do that? or Do we only do that when the first term of the power series is a constant and thus when it is...

Hi, I am trying to do the multipole expansion of a point charge away from the origin, I can't understand Legendre polynomials so want to do it in Cartesian but when I try to Taylor expand the \left|\frac{1}{\vec{r}-\vec{r'}}\right| I am not sure how to handle the modulus. Any help...

Homework Statement Let's say A is a 7x7 matrix which is defined as [a b c 0 0 0 0; b a 0 d 0 0 0; c 0 a b e 0 0; 0 d b f 0 e 0; 0 0 d 0 f b g; 0 0 0 d b f h; 0 0 0 0 0 0 0] where semicolon (;) represent a new row and a space is a new column.Homework Equations If y = expm (A*t), where expm...

Hello :smile: I'm currently using past papers to revise for January exams, and I've found a bit of a problem with something I thought I was okay with. Homework Statement The position at time t of a particle undergoing damped oscillations is given by: x = 2e^{-t}\sin(3t). Express...

Planck's radiation law: I(\lambda)=\frac{2\pi hc^2}{\lambda^5(e^{\frac{hc}{\lambda kT}}-1)} I'm trying to calculate the peak of a graph, so setting the derivative equal to 0, I've gotten it down to \frac{\lambda(e^{\frac{\alpha}{\lambda}}-1)}{e^{\frac{\alpha}{\lambda}}}=\frac{\alpha}{5}...

In equation 5.8 in this document http://www.damtp.cam.ac.uk/user/tong/qft/qft.pdf I am trying to derive this Hamiltonian. I find H= \pi \dot{\psi} - L = i \psi^\dagger \dot{\psi} - \bar{\psi} ( i \gamma^\mu \partial_\mu - m ) \psi = i \bar{\psi} \gamma^0 \partial_0 \psi - i \bar{\psi}...

Differentiating an equation! Homework Statement How do I differentiate this V(x) = 300x * sqrt(1296-x^2) The Attempt at a Solution I tried using the product rule but that didnt work at all PLease help Thank you so much!

I'm in real analysis classes but my calculus is shaky when I hit things that aren't plug and chug. How do you evaluate this integral and why can you ignore the dx differential? The more theoretical details, it smells like some flavor of the Fundamental Theorem of Calculus or Leibniz's Rule...

According to Kant's synthetic a priori what differences would lie between intelligent design AND certain interpretations of physical principles such as, but not limited to, multiple universe ideas? and Does Kant's reasoning even hold water when comparing the two? IMO, it does apply and no...

Homework Statement (2x-10+e)^(y+8)=e^(x-6) value of dy/dx at the point, (5,-9) Homework Equations The Attempt at a Solution (y+8)ln(2x-10+e)=x-6 y' ln(2x-10+e)+(y+8)(2+e)/(2x-10+e)=1 ln(2*5-10+e)=1 y'+(-9+8)(2+e)/e=1 y'-(2+e)/e=1 y'=1+(2+e)/e but the answer is (2+e)/e, I don't know where i...