Suppose u(t)=w(t^2+2) and w’(3)=8 Find u’(1)

Answer 1

u(t) = w(t² + 2)

By the Chain Rule, u'(t) = w'(t² + 2) (t² + 2)' = 2t w'(t² + 2)

So, u'(1) = 2(1) w'(3) = 2(8) = 16