Read about differentiation | 60 Discussions | Page 1

The Attempt at a Solution I know the answer is supposed to be ##(-1,0)##. However when I differentiate the above expression I get. $$ 2x+{\frac 5 2} $$ Then the shortest distance would be when the expression equates to 0. $$ 2x+{\frac 5 2}=0 $$ I should be getting ##x=-1## but solving for ##x##...

The working I've tried is in the attachment.

If we have two functions C(y(t), r(t)) and I(y(t), r(t)) can we write $$\frac{\frac{dC}{dt}}{\frac{dI}{dt}}=\frac{dC}{dI}$$?

I found a theorem that states that if A and B are 2 endomorphism that satisfies $$[A,[A,B]]=[B,[A,B]]=0$$ then $$[A,F(B)]=[A,B]F'(B)=[A,B]\frac{\partial F(B)}{\partial B}$$. Now i'm trying to apply this result using the creation and annihilation fermionics operators $$B=C_k^+$$ and $$A=C_k$$...

Calculation of Fourier Transform Derivative d/dw (F{x(t)})=d/dw(X(w)) Hello to my Math Fellows, Problem: I am looking for a way to calculate w-derivative of Fourier transform,d/dw (F{x(t)}), in terms of regular Fourier transform,X(w)=F{x(t)}. Definition Based Solution (not good enough): from...

I first solved the first two terms and then i solved the resulting term with the third term and so on.At last i was left with x^n/((x-a1)(x-a2)...(x-an)) .Thrn i took log on both sides and then differentiated both sides with respect to x.I got 1/y dy/dx=n/x -1/(x-a1)-1/(x-a2)...-1/(x-an).But now...

My Question : Shouldn't differentiating ##-log B## give ##\frac{-\delta B}{B}##? (Note : A, B and Z are variables not constants) By extension for ##Z=A^a \,B^b\, C^c## where ##c## is negative, should ##\frac{\Delta Z}Z=|a|\frac{\Delta A}A+|b|\frac{\Delta B}B-|c|\frac{\Delta C}C##?

Homework Statement [/B] From the Rodrigues’ formulae, I want to derive nature of the spherical Bessel and Neumann functions at small values of p. Homework Equations [/B] I'm going to post an image of the Bessel function where we're using a Taylor expansion, which I'm happy with and is as far...

Hi all, I was working on a problem using Euler-Lagrange equations, and I started wondering about the total and partial derivatives. After some fiddling around in equations, I feel like I have confused myself a bit. I'm not a mathematician by training, so there must exist some terminology which...

I'm confused about the mathematics that led to the equation 4.5.9. Specifically, I'm confused about what the variables that describe U are. From the equation I think temperature T(through beta), chemical potential (through alpha), V (through E_s) and N (through... restriction on the...

Homework Statement See question number 3 Homework Equations Work Done="integral" F*ds The Attempt at a Solution I tried to solve this question using integration, I have replaced F with "1" and ds with "t^2+2t". So I am stuck in at that step. Please help me differentiate it further or solve...

Homework Statement I am facing problem in applying the chain rule. The question which I am trying to solve is, " Find the second derivative of " Homework Equations The Attempt at a Solution So, differentiated it the first time, [BY CHAIN RULE] And now to find the second derivative I...

Could someone explain to me how from this graph you can deduce that ##\tan(\theta) = \frac {df} {dx}##. Thanks

Question: Question: Find the point on the curve y=x^2 +1 that is closest to the point (18,1). Please see the image and that’s where I’m stucked- after taking the first derivate. Please solve it further step by step completely. It’d mean a lot.

1. The problem statement, all variables, and given/known data Find and categorize extremes of the following function: $$F(y)=\int_{y}^{y^{2}}\frac{1}{\ln^{2}x}dx$$ for ##y>1##. Homework Equations $$\frac{d}{dx}\int_{a}^{b}f(x,y)dy=\int_{a}^{b}\frac{\partial}{\partial x}\left(f(x,y)\right)dy$$...

I am trying to find out the interference condition between tool and a part. The below attached snapshot is the equation between interference and machine feed. At dy/dx = 0, I will have max. interference, which I intend to find. Except x and y every alphanumeric character in the following...

Homework Statement I have a system of coupled differential equations representing chemical reactions and given certain initial conditions for the equations I can observe oscillation behaviour when I solved the equations numerically using Euler's Method. However, then it asks to investigate the...

Hi, I was just wondering how one would arrive at the answers to these questions. I have the solution for parts a and b, but not for part c. Suppose that antibiotics are injected into a patient to treat a sinus infection. The antibiotics circulate in the blood, slowly diffusing into the sinus...

Homework Statement The radius of a circle increases from 3 to 3.01 cm. Find the approximate change in its perimeter. Here's a link to the actual question, in case you need the answer for 6(a) to solve 6(b) http://imgur.com/a/nQt6M Homework Equations Perimeter of circle = 2πr Area of circle =...

I thought Differentiation is all about understanding it in a graph. Every time I solve a question on differentiation I visualise it as a graph so it's more logical. After all, that IS what the whole topic is about, right? Or am I just wrong? But when you look at these questions...

Homework Statement [/B] 2. The attempt at a solution I'm not really sure where to start. We just want to show that ##\lim_{x \to c} \frac{f(x) - f(c)}{x - c} = 0##. I see that ##\lim_{x \to c} (x - c)^2 = 0##. I feel that this may be a simple trick of inequalities, but I am having a complete...

Homework Statement ##x^3 - 4x^2 + ax + b## tangent to x-axis at x = 3 Homework Equations The Attempt at a Solution if the graph tangent at x = 3, means at x =3, y = 0 my questions is, is at x = 3 the graph's gradient (slope) = 0 ? if yes why? if yes then means dy/dx = 0 ##3x^2 - 8x + a =...

Homework Statement Hello I have this circle with the equation : [/B] (x-a)^2+(y-b)^2=r^2 I want to find dy/dx for it 2. Homework Equations (x-a)^2+(y-b)^2=r^2 The Attempt at a Solution I am looking on the internet and it appears that I should use what is called "Implicit differentiation"...

Homework Statement : [/B]find the dy/dx of xy=a constant Homework Equations : basic differentiation formulae[/B] The Attempt at a Solution :[/B] I know we can use logarithmic differentiation for differentiating x y..But can we differentiate it using chain rule and get answer as...

Dear friends, I have found a derivation of the fact that, under the assumptions made in physics on ##\rho## (to which we can give the physical interpretation of charge density) the function defined by $$V(\mathbf{x},t):=\frac{1}{4\pi\varepsilon_0}\int_{\mathbb{R}^3}...

Homework Statement This is my 'carrying out a practical investigation' assignment for Maths. I've attached the coursework (what I've wrote up to now) and my main concern is whether I've got the right differential equation to find 3 new velocity values throughout the pendulum trajectory...

I'm using this method: First, write the polynomial in this form: $$a_nx^n+a_{n-1}x^{n-1}+......a_2x^2+a_1x=c$$ Let the LHS of this expression be the function ##f(x)##. I'm gonna write the Taylor series of ##f^{-1}(x)## around ##x=0## and then put ##x=c## in it to get ##f^{-1}(c)## which will be...

Could someone please help me work through the differentiation in a paper (not homework), im having trouble finding out how they came up with their cost function. The loss function is L=wE, where E=(G-Gest)^2 and G=F'F The derivative of the loss function wrt F is proportional to F'(G-Gest)...

andrewkirk submitted a new PF Insights post Partial Differentiation Without Tears Continue reading the Original PF Insights Post.

Homework Statement a. Given u=F(x,y,z) and z=f(x,y) find { f }_{ xx } in terms of the partial derivatives of of F. b. Given { z }^{ 3 }+xyz=8 find { f }_{ x }(0,1)\quad { f }_{ y }(0,1)\quad { f }_{ xx }(0,1) Homework Equations Implicit function theorem, chain rule diagrams, Clairaut's...