Differentiating Definition and 262 Threads

Here's what I have so far: std::string CalculusWizard::derivative(std::string& fx, const char & x, unsigned & n = 1) { if (n == 0) { return fx; } else if (n > 1) { while (n-- > 1) fx = derivative(fx, x); } // If here, find and return the derivative of fx ...

Here is the question: I have posted a link there to this thread so the OP can view my work.

Marxian economics: Differentiating the "Rate of Profit Equation" While watching a recent Youtube video on Marxian crisis theory and the Tendency Of The Rate Of Profit To Fall, I decided to apply calculus to the equations to see what I got. The rate of profit is defined as ∏ = S / (C...

Homework Statement I have the functionu(x,t)=\frac{1}{2c}\int^{x+ct}_{x-ct}g(\xi)d\xiwhere g is continuously differentiable and c is a constant. I need to verify that this is a solution to the wave equation. Homework Equations My prof gave me the...

Suppose I have something like $$\frac{-2(t - 1)}{9t^5}$$ I know I just plug in two points to check its concavity...But How do I know what to choose between what and what? Like would I just choose between 0 and 1? And how do I know ? Also suppose I have something like $$ - \frac{1}{4t^3}$$...

Homework Statement In oppgave 1 a) I am supposed to show that the given equality is true (namely that the isoterm compressibility coefficient partial-differentiated with regards to temperature = isobar coefficient differentiated with regards to pressure multiplied by minus one)...

Hi, I figured out the only redundancy to my problem is this: I'll start off with a simple case, where w1,w2 are the displacements at intervals of one third along a beam. w = 3w1/L.x (Note, x is in the numerator for all cases) To differentiate this with respect to time, I use the...

In my high school Calculus course, I've encountered several optimization problems involving the area of a circle and I noticed the obvious fact that if you differentiate the area of a circle you obtain the expression for its circumference. This implies that the rate of change of a circle's area...

So the question is…Evaluate the following… $$\frac{d}{dx} \left(\int _1^{x^2} \cos(t^2) \, dt \right)$$ I thought i could use the FTC on this because it states… $$\frac{d}{dx} \left(\int_0^x f(t)\, dt \right)=f(x)$$ but i can't correct? because in my question it starts at 1…is there some way...

I have to solve a bunch of exercises related to function series and in some of them they ask me whether a particular series converges uniformly if one differentiates it term by term. So here I came up with a doubt: When ##\sum_0^{\infty} f_n(x)## can be differentiated term by term? What...

Say I have a simple series like \Sigma^{∞}_{n=0} X^{n} When I differentiate this series the first term goes to 0 because it's a constant. Does that mean that I have to adjust the index of the series from n=0 to n=1? If I don't do it, the first term still goes to zero as n(x^(n-1)) when n=0...

Sorry, I did not know where to post this as it is sort of a "philosophy of physics" question that I am not sure has an answer and was curious if anyone had any thoughts not grounded in pseudoscience. How can a set of particles interacting in quantum fashion (perhaps a bose einstein condensate...

something I often see without justification in my physics books. What is the justification for the following convolution property (pulling the derivative inside the integral) (f*g)^\prime = \frac{d}{dx} \int f(x) g(x-u) dx = \int f(x) \frac{d}{dx} g(x-u) dx = f(x) * g(x)^\prime

Here is the question: I have posted a link there to this topic so the OP can see my work.

Dear all, I just wondered whether there was any standard identity to help me solve this equation: $$ \int \delta(f(x))^{\prime\prime}g(x) dx $$ Thanks in advance for your help.

Hi. So I have this vector function which I need to differentiate, it is however very tricky to do by hand, so I'm doing it in Mathematica. \hat{u}=\left\langle\bar{u}+\bar{r}\frac{(1+\gamma)}{r(r+\bar{u}\cdot \bar{r})}\right\rangle (The brackets denote normalisation) I want to do this...

Spectral redshift is currently understood to be of a variety of sources, velocity / doppler redshift, gravitational redshift, cosmological redshift, etc. Is there any ability to tell,purely from the spectral analysis of the light itself, without knowing what the source of the light is, what...

The textbook says that differentiating a sinusoid is the same as multiplying the phasor by jω. Shouldn't jω be jωejωt?

Homework Statement A small commuter plane has 30 seats. The probability that any particular passenger will not show up for a flight is 0.10, independent of other passengers. The airline sells 32 tickets for the flight. Calculate the probability that more passengers show up for the flight...

I came across this simple expression while doing some maths. If \frac{d}{dx}f(x)=g(x) Then \frac{d}{dx}f(-x)=-g(-x) Is this correct? How do we prove it?

I am attempting to work my way through the product rule for inner products, using the properties of linearity and symmetry. I am wondering if the following step is allowed, exploiting the bilinear property: f(t) = \left\langle{\alpha}(t),{\beta}(t)\right\rangle \rightarrow f'(t) = \lim_{h \to...

Homework Statement Sin(tan(2x)) With respect to x Homework Equations Differentiation The Attempt at a Solution My question is whether I can simply use d/dx (Tan x) = Sec^2(X) to extrapolate that to d/dx(tan 2x) = Sec^2(2x) ? Or do I have to convert to sine/cosine and go from...

How do i derivate e^e^x (I don't know how to type it on latex but here you can se what i mean e^e^x - Wolfram|Alpha Results basicly don't know how I shall think

Homework Statement Obtain an expression for the potiential energy between to particles in an ionic bond at radius r0 Homework Equations Coloumb's laws: F = (-k * q1 * q2)/r-1The Attempt at a Solution I think that if i do U = r0∫0 F(r)dr = [k * q1 * q2 * r-1]r00 = k * q1 * q2 * r0-1, Then that's...

Homework Statement I have a problem where I have a mass suspended in a system of springs. I need to differentiate the equation wrt time so I can can show equivalence with Newton's second law. The mass and springs are vertically aligned so the motion is in one dimension. The actual problem has...

A particle of mass m is moving along the x-axis and experiences a force F(x), also along the x-axis, given by F(x) = -kx. Deduce an expression for the potiential energy of the particle. I tried intergrating both side (just to see if it gave me anything helpful). I got ∫F(x)dx=mv for the...

How do we show that \frac{d}{dt}\left[\int\!y\,\mathrm{d} x\right] = y\,\frac{dx}{dt}

Here was my thinking for differentiation (which, by the way, is wrong): By the definition of the function, the following equations are equal: $$W(xe^x)=x$$ By the chain rule and product rule: $$\frac{dW}{dx}( e^x+xe^x ) =1$$ $$\frac{dW}{dx}=(e^x+xe^x)^{-1}$$ What is the error here? What is...

Hello everyone! I've came across this problem: differentiate $\int _S f \ln f$ with respect to $f$. From previous explanation, I believe $\int _S f \ln f$ means $\int _S f(x) \ln f(x)dx$. The answer is $\ln f(x)$... Could anyone indicate how they reached this answer? Thanks!

Homework Statement Differentiate: v = 3t^2 - 14t + 8The Attempt at a Solution I am not sure if you do anything with the constant "+ 8" is it ignored when differentiating? if its ignored then the answer is: a = \frac{dv}{dt} = 6t - 14

I don't have a ton of experience in numerical methods, so I'm hoping someone can help me out. Suppose I have a sequence of position data points for a car, but they've been truncated to integer values. I want to find the speed (derivative), but for speeds which are low relative to the time...

Homework Statement Differentiate V0 - iR - q/C = 0 to prove that di/dt = -i/RC. Homework Equations V0 - iR - q/C = 0 ^ derived from previous question for a circuit that had one battery with emf V0, a resistor of resistance R and a capacitor of capacitance C (all in series). di/dt =...

Suppose I have a really simple first order linear ODE like:$$\dot{\omega} = -k\omega$$ where k is some constant, ω(t) is a function of time that I want to solve for, and the overdot denotes the derivative w.r.t. time. This is really easy to solve, and we all know that with the initial condition...

I know how to differentiate the dot and cross products of two vectors, is the differentiation of a vector sum done like this: d/dt (u+t) = u' + t + u + t' Or simply add them and then differentiate? Thanks

Hi, I am having some trouble understanding what I have done here, or if it makes any sense at all. Recall that \frac{d^a}{dx^a}x^k = \frac{\Gamma(k+1)}{\Gamma(k-a+1)}x^{k-a} We can extend this to complex numbers if we let a be of the form p + qi, where p and q are real, and i is the imaginary...

Hello! The picture says a thousand words: http://www.hot.ee/jaaniussikesed/v6rrand.jpg In the last member under the square root, there is the error. For some reason I am not able to differentiate with an array index, ts1 is a single column 5 row matrix. How to solve this? The error says...

What are rules for differentiating a Fourier series? For example, given $$ f = \frac{4}{\pi}\sum_{n=1}^{\infty}\frac{\sin(2n-1)\theta}{2n-1} = \begin{cases} 1, & 0 < \theta < \pi\\ 0, & \theta = 0, \pm\pi\\ -1, & -\pi < \theta < 0 \end{cases} $$ Can this be differentiating term wise? If so...

differentiating to find one unknown function out of three?? Homework Statement Hi everyone I need some help with a question that i have solved yet i find it hard to understand. I have three given functions in the picture attached. All three consist of one single graph. And they give me...

What is the difference? I always see differentiate a function but never an equation, a lot of exercises have y=blahblah which is an equation. Does it just mean that when you're asked to differentiate the equation (without using implicit), that it is satisfies the conditions for a function?

Differentiating y=x^x x=ln(y) I changed the base to e x=\frac{ln(y)}{ln(x)} xln(x) = ln(y) e^{xln(x)} = y e^{xln(x)}(1+ln(x) = \frac{dy}{dx} The answer the calculator got was x^{x(1+ln(x))} so I noticed that since y=x^x and e^{xln(x)} = y, then I could replace it with x^x in the final answer...

Somebody want to help with this derivative: y = (7.75x3 + 2250) / 750x I differentiate it with the quotient rule and get: dy/dx = 31x / 1500 - 3 / x2 But that's wrong. It's got a zero around 5 - 6 and the original function has its minimum at (4.03, 1.12). Not sure what I did wrong.

Differentiating the term: (x2-1)u' n+1 times gives (according to my book): (x2-1)u(n+2) + 2x(n+1)u(n+1) + n(n+1)u(n) Now I see how the first two parts arise. However, I don't really understand the last one - or more specifically I don't understand how you find that un appears exactly...

So, when you differentiate a function, specifically an explicit function, where y is a function of x, you are differentiating each term with respect with x. Well, when you differentiate x with respect with x, does that mean you are trying to find out how x changes with x? What does that mean...

They give a differential equation: x' = f_a(x) = ax(1-x) . In determining if the equilibrium points are sources or sinks, they say: We may also determine this information analytically. We have f'_a(x) = a - 2ax How can they differentiate with respect to x? x is a function, it doesn't...

Homework Statement Find the derivative of (x^2)(sinx)(tanx) Homework Equations f(x+y)(d/dx)=(x)(y)d/dx+(y)(x)d/dx That's for differentiating with 2 terms. With 3, I haven't done it yet. The Attempt at a Solution x^2(sinx)(sec^2x)+tanx(sinx)2x+x^2(tanx)(cosx)...

Homework Statement (See attached figure) I need to find V0 in terms of R1, R2, R3 and C.Homework Equations V0 = -RC (dVs/dt) for a differentiatorThe Attempt at a Solution I understand I have to apply KCL at the node between C and R1, and I've also determined that R1 and R2 are in series (not...

1. I have this equation: y= 2.52e^-0.8472x which I need to differentiate. 2. I am unsure whether to use the product or chain rule> 3. I honestly don't know what to do... I was thinking 2.52e^u?

Homework Statement f(x) = 2x * (10-x^2)^(1/2) Determine f'(x). 2. The attempt at a solution f'(x) = 2x*(1/2) * (10-x^2)^(-1/2) * (-2x) = x * (-2x) * (10-x^2)^(-1/2) = -2x^2 * (10-x^2)^(-1/2) What am I doing wrong?

I'm trying to differentiate 2^(x^2), but I'm getting a factor of two out and can't figure out why. I approached the question as follows.. y=2^(x^2) , so y=(2^x)^x u=2^x y=u^x du/dx = (2^x)ln2 dy/du = xu^(x-1) = x(2^x)^(x-1) = x(2)^((x^2)-x) So dy/dx =...

Homework Statement let z=f(x,y) be a differentiable function. If we change to polar coordinates, we make the substitution x=rcos(θ), y=rsin(θ), x^2+y^2=r^2 and tan(θ) = y/x. a. Find expressions ∂z/∂r and ∂z/∂θ involving ∂z/∂x and ∂z/∂y. b. Show that (∂z/∂x)^2 + (∂z/∂y)^2 = (∂z/∂r)^2 +...