Mathematics

Problem

Let

f(x)=\dfrac{x^{2}\tan x+\sin x}{x+1}

. a. (i) Differentiate the numerator

N(x)=x^{2}\tan x+\sin x

. Simplify your result. b. (ii) Differentiate the denominator

D(x)=x+1

. State the derivative clearly. c. (iii) Hence obtain

f'(x)

using an appropriate rule and simplify the final answer so that no factor remains common in the numerator.