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

Explanation

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

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