Answer :
Differentiating with respect to x
f’(x)= sinx + xcosx
Differentiating with respect to x
f’’(x) = cosx +cosx – xsinx
= -sinx + 2cosx
(ii) e2x cos 3x
Differentiating with respect to x
f’(x) = 2e2xcos3x + e2x(-sin3x).3
= 2e2xcos3x – 3e2xsin3x
Differentiating with respect to x
f’’(x) = 2.2e2xcos3x + 2e2x(-sin3x).3 – 3.2e2xsin3x – 3e2xcos3x.3
= 4e2xcos3x - 6e2xsin3x – 6e2xsin3x – 9e2xcos3x
=-12e2xsin3x – 5e2xcos3x
(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
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