If y = x sin x, find δyδx

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

Answer Details

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