derivative

1. 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 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. 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...

8. 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 ...

29. 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. 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...