Given the functions and

MATHEMATICS · Multi-part · A Level · Mathematics · Differentiation · Differentiation

Problem

Given the functions

f(x)=\sin (x^{2})

and

g(x)=\sin ^2 x

, answer the following: (i) Find

f'(x)

. (ii) Find

g'(x)

. (iii) State one reason, based on the results of parts (i) and (ii), why the two derivatives are structurally different even though

f(x)

and

g(x)

look similar.