1. Matt & Hugh play with a Brick and derive Centripetal Acceleration

    Matt & Hugh play with a Brick and derive Centripetal Acceleration

    Matt and Hugh play with a tennis ball and a brick. Then they do some working out to derive the formula for the centripetal force (a = v^2/r) by differentiati...
  2. A

    A Calculation of Fourier Transform Derivative d/dw (F{x(t)})=d/dw(X(w))

    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...
  3. L

    I Understanding the definition of derivative

    As far as I understand, when we want to differentiate a vector field along the direction of another vector field, we need to define either further structure affine connection, or Lie derivative through flow. However, I don't understand why they are needed. If we want to differentiate ##Y## in...
  4. hilbert2

    I Idea about single-point differentiability and continuity

    Many have probably seen an example of a function that is continuous at only one point, for example ##f:\mathbb{R}\rightarrow\mathbb{R}\hspace{5pt}:\hspace{5pt}f(x)=\left\{\begin{array}{cc}x, & \hspace{6pt}when\hspace{3pt}x\in\mathbb{Q} \\ -x, &...
  5. S

    I Velocity, acceleration, jerk, snap, crackle, pop, stop, drop, roll...

    Edit: I see this was discussed in the related thread sorry for a repost. If acceleration causes a change in velocity, and jerk causes a change in acceleration, snap causes a change in jerk, crackle causes a change in snap, pop causes a change in crackle, stop causes a change in pop, drop causes...
  6. fazekasgergely

    Infinite series to calculate integrals

    For example integral of f(x)=sqrt(1-x^2) from 0 to 1 is a problem, since the derivative of the function is -x/sqrt(1-x^2) so putting in 1 in the place of x ruins the whole thing.
  7. SamRoss

    B Justification for cancelling dx in an integral

    In Paul Nahin's book Inside Interesting Integrals, on pg. 113, he writes the following line (actually he wrote a more complicated function inside the integral where I have simply written f(x))... ## \int_0^\phi \frac {d} {dx} f(x) dx =...
  8. navneet9431

    Evaluating This limit

    <Moderator's note: Moved from a technical forum and thus no template.> $$\lim_{x\rightarrow 0} (x-tanx)/x^3$$ I solve it like this, $$\lim_{x\rightarrow 0}1/x^2 - tanx/x^3=\lim_{x\rightarrow 0}1/x^2 - tanx/x*1/x^2$$ Now using the property $$\lim_{x\rightarrow 0}tanx/x=1$$,we have ...
  9. U

    I Boundedness of derivatives

    Hi forum. I'm trying to prove a claim from Mathematical Analysis I - Zorich since some days, but I succeeded only in part. The complete claim is: $$\left\{\begin{matrix} f\in\mathcal{C}^{(n)}(-1,1) \\ \sup_{x\in (-1,1)}|f(x)|\leq 1 \\ |f'(0)|>\alpha _n \end{matrix}\right. \Rightarrow \exists...
  10. Jozefina Gramatikova

    I How to differentiate with respect to a derivative

    Hi guys, I am reading my lecture notes for Mechanics and Variations and I am trying to understand the maths here. From what I can see there we differentiated with respect to a derivative. Could you tell me how do we do that? Thanks
  11. A different perspective to derivatives rather than slopes-3b1b

    A different perspective to derivatives rather than slopes-3b1b

    A different perspective to derivatives.
  12. YoungPhysicist

    Rookie derivative question

    1. Homework Statement ##f(x) = (5x+6)^{10} , f'(x)=?## 2. Homework Equations ##\frac{d}{dx}x^n = nx^{n-1}##? 3. The Attempt at a Solution I do know the solution ##f'(x) = 50(5x+6)^9##,but I don't know how this solution came to be.I downloaded this problem from the web and it only comes with...
  13. SebastianRM

    I What is the 'formal' definition for Total Derivative?

    A total derivative dU = (dU/dx)dx + (dU/dy)dy + (dU/dz)dz. I am unsure of how to use latex in the text boxes; so the terms in parenthesis should describe partial differentiations. My question is, where does this equation comes from?
  14. J

    Determine the period of small oscillations

    1. Homework Statement Two balls of mass m are attached to ends of two, weigthless metal rods (lengths l1 and l2). They are connected by another metal bar. Determine period of small oscillations of the system 2. Homework Equations Ek=mv2/2 v=dx/dt Conversation of energy 2πsqrt(M/k) 3. The...
  15. YoungPhysicist

    B Is this a valid proof?

    Recently I came up with a proof of “ for a nth degree polynomial, there will be n roots” Since the derivative of a point will only be 0 on the vertex of that function,and a nth degree function, suppose ##f(x)##has n-1 vertexes, ##f’(x)## must have n-1 roots. Is the proof valid?
  16. M

    A Differential of a function

    We define the differential of a function f in $$p \in M$$, where M is a submanifold as follows In this case we have a smooth curve ans and interval I $$\alpha: I \rightarrow M;\\ \alpha(0)= p \wedge \alpha'(0)=v$$. How can I get that derivative at the end by using the definitions of the...
  17. D

    Derivative of expanded function wrt expanded variable?

    Homework Statement If I have the following expansion f(r,t) \approx g(r) + \varepsilon \delta g(r,t) + O(\varepsilon^2) This means for other function U(f(r,t)) U(f(r,t)) = U( g(r) + \varepsilon \delta g(r,t)) \approx U(g) + \varepsilon \delta g \dfrac{dU}{dg} + O(\varepsilon^2) Then up to...
  18. Math_QED

    I Two questions about derivatives

    In Rudin, the derivative of a function ##f: [a,b] \to \mathbb{R}## is defined as: Let ##f## be defined (and real-valued) on ##[a,b]##. For any ##x \in [a,b]##, form the quotient ##\phi(t) = \frac{f(t) - f(x)}{t-x}\quad (a < t <b, t \neq x)## and define ##f'(x) = \lim_{t \to x} \phi(t)##, if the...
  19. Phylosopher

    I Is the exponential function, the only function where y'=y?

    Hello, I was wondering. Is the exponential function, the only function where ##y'=y##. I know we can write an infinite amount of functions just by multiplying ##e^{x}## by a constant. This is not my point. Lets say in general, is there another function other than ##y(x)=ae^{x}## (##a## is a...
  20. I

    B Understanding this graph

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

    I Relationship between force and potential energy

    I am aware that the negative derivative of potential energy is equal to force. Why is the max force found when the negative derivative of potential energy is equal to zero?
  22. R

    Calculus derivatives word problem

    1. Homework Statement Is it possible to accurately approximate the speed of a passing car while standing in the protected front hall of the school? Task: Determine how fast cars are passing the front of the school. You may only go outside to measure the distance from where you are standing to...
  23. shintashi

    B When do we use which notation for Delta and Differentiation?

    I was taking notes recently for delta y/ delta x and noticed there's more than one way to skin a cat... or is there? I saw the leibniz dy/dx, the triangle of change i was taught to use for "difference" Δy/Δx, and the mirror six ∂f/∂x which is some sort of partial differential or something...
  24. EastWindBreaks

    Derivative of x(t)?

    1. Homework Statement 2. Homework Equations 3. The Attempt at a Solution I am trying to repair my rusty calculus. I dont see how du = dx*dt/dt, I know its chain rule, but I got (du/dx)*(dx/dt) instead of dxdt/dt, if I recall correctly, you cannot treat dt or dx as a variable, so they...
  25. M

    Interpret success-rate/time * $

    1. Homework Statement You are applying for a ##\$1000## scholarship and your time is worth ##\$10## an hour. If the chance of success is ##1 -(1/x)## from ##x## hours of writing, when should you stop? 2. Homework Equations Let ##p(x)=1 -(1/x)## be the rate of success as a function of time...
  26. rishi kesh

    Derivative of -x using first principle

    1. Homework Statement This is a silly question,but i have a problem.How do we solve derivative of -x using first principle of derivative. I know that if derivative of x w.r.t x is 1 then ofcourse that of -x should be -1. Also it can be solved by product rule taking derivative of -1.x . 2...
  27. rishi kesh

    How to find the derivative of this function

    1. Homework Statement How do we find the derivative of function: y= √[(1-sinx)/(1+sinx)] This is the exercise problem from my textbook. I have not covered chain rule yet. So please you basic derivative rules to solve it. 2. Homework Equations Here is the answer of derivative given in my...
  28. aphirst

    I Derivative and Parameterisation of a Contour Integral

    As part of the work I'm doing, I'm evaluating a contour integral: $$\Omega \equiv \oint_{\Omega} \mathbf{f}(\mathbf{s}) \cdot \mathrm{d}\mathbf{s}$$ along the border of a region on a surface ##\mathbf{s}(u,v)##, where ##u,v## are local curvilinear coordinates, and where the surface itself is...
  29. T

    Finding the min value using the derivative

    1. Homework Statement Hi I'm having a trouble with finding min value of given function: f(x) = sqrt((1+x)/(1-x)) using derivative. First derivative has no solutions and it is < 0 for {-1 < x < 1} when f(x) is given for {-1 < x <= 1}. For x = - 1 there is a vertical asymptote and f(x) goes to...
  30. A

    I Why does this concavity function not work for this polar fun

    For the polar equation 1/[√(sinθcosθ)] I found the slope of the graph by using the chain rule and found that dy/dx=−tan(θ) and the concavity d2y/dx2=2(tanθ)^3/2 This is a pretty messy derivative so I checked it with wolfram alpha and both functions are correct (but feel free to check in case...