If y = x sin x, find \(\frac{\delta y}{\delta x}\)

A.

sin x - cos x

B.

cos x - x sin x

C.

cos x + x sin x

D.

sin x + x cos x

Correct answer is D

y = x sin x

Where u = x and v = sin x

Then \(\frac{\delta u}{\delta x}\) = 1 and \(\frac{\delta v}{\delta x}\) = cos x

By the chain rule, \(\frac{\delta y}{\delta x} = v\frac{\delta u}{\delta x} + u\frac{\delta v}{\delta x}\)

= (sin x)1 + x cos x

= sin x + x cos x