Find the Fourier series of f (x)= x^3 in x = Π to Π Watch later Share Copy link Info Shopping Tap to unmute If playback doesn't begin shortly, try restarting your device Up next In order to find for any function f(x), we must apply the 'transformation' y=x In order to do that, we must define x in terms of y, ie, find f(y), then set y=x Let y=f(x) y=(x3)^31 y1=(x3)^3 x3=root(3)(y1) x=3root(3)(y1) We've now found f(y), so we must set y=x by replacing x with y and y with x f^1(x)=y=3root(3)(x1) Explanation First of all, let's compute the derivative of f (x), indicated as f '(x) f (x) = − x3 −3 ⇒ f '(x) = −3x2 In fact, to derive a sum you must derive each single term The first term is a power of x, and the derivative of xn is nxn−1 So, the derivative of x3 is 3x3−1 = 3x2, and since we had a minus sign in front of it, we will have to change signs the derivative of −x3 is −3x3−1 = −3x2
Verifying Inverse Functions By Composition Not Inverse Video Khan Academy
