Question

differentiate this question y=( x square+x sinx)power 5/2

Answer 1

\[y=\left(x^2+x\sin(x)\right)^{\frac{5}{2}}\]?

Answer 2

chain rule, then product rule for inside piece
\[y'=\frac{5}{2}\left(x+x\sin(x)\right)^{\frac{3}{2}}\frac{d}{dx}[x+x\sin(x)]\]

Answer 3

then
\[\frac{d}{dx}[x+x\sin(x)] =1+\sin(x)+x\cos(x)\] so final answer is
\[y'=\frac{5}{2}\left(x+x\sin(x)\right)^{\frac{3}{2}}\left(1+\sin(x)+x\cos(x)\right)\]