Use the Chain Rule to express the second derivative of 𝑓∘𝑔 in terms of the first and second derivatives of 𝑓 and 𝑔.

Answer 1

Hello Ash L!

If say H(x)=f(g(x))

Then by the chain rule

H'(x)=f'(g(x))*g'(x)

By the product rule:

H''(x)=[f'(g(x))]'*g'(x)+f'(g(x))g''(x)

H''(x)=f''(g(x))*(g'(x))^2+f'(g(x))*g''(x)