Mathematics

Problem

Let

h(x)=x\sin x

. (i) Evaluate

\dfrac{d}{dx}(x)

and

\dfrac{d}{dx}(\sin x)

x=0

. (ii) Compute

h'(0)

. (iii) Explain why the result in part (ii) can be zero even though each derivative found in part (i) is non-zero at

x=0