Question

Find f'(x) when f(x)=sin(1/x^3)

Answer 1

let z = 1/x^3 = x^(-3) then dz/dx =-3 x^-4

then f(z) = sin z
d f(z)/dz = cos z = cos(1/x^3)
d f(x)/dx = df(z)/dz * dz/dx
so
(-3/x^4) cos (1/x^3)