Differentiating with respect to x

f’(x)= sinx + xcosx

Differentiating with respect to x

f’’(x) = cosx +cosx – xsinx

= -sinx + 2cosx

(ii) e^2x cos 3x

Differentiating with respect to x

f’(x) = 2e^2xcos3x + e^2x(-sin3x).3

= 2e^2xcos3x – 3e^2xsin3x

Differentiating with respect to x

f’’(x) = 2.2e^2xcos3x + 2e^2x(-sin3x).3 – 3.2e^2xsin3x – 3e^2xcos3x.3

= 4e^2xcos3x - 6e^2xsin3x – 6e^2xsin3x – 9e^2xcos3x

=-12e^2xsin3x – 5e^2xcos3x

(iii) x³ log x

Differentiating with respect to x

f’(x) =

f’(x) = 3x²log x + x²

Differentiating with respect to x

= 6x log x + 3x +2x

= 6x log x +5x