A student differentiates the function as follows: Step 1

MATHEMATICS · Subjective · A Level · Mathematics · Differentiation · Differentiation

Problem

A student differentiates the function

h(x)=x^{2}\cos x

as follows: Step 1

h'(x)=2x\cos x+x^{2}(-\sin x)

. Step 2

h'(x)=2\cos x-x\sin x

. (i) Identify and explain the error made in Step 2. (ii) Write the correct simplified form of

h'(x)

. (iii) For

x=\dfrac{\pi}{4}

, compute the correct numerical value of

h'(x)

to two decimal places.