Find `(dy)/(dx)` for the functions: `y=x^3e^xsinx`

Answer

`x^(2)e^(x)(3 sin x + x sin x + x cos x )`

Explanation

`y=x^(3)e^(x) sin x`
`therefore" " (dy)/(dx)=(d)/(dx)(x^(3)e^(x)sin x)`
`={(d)/(dx)(x^(3))}e^(x) sin x +x^(3){(d)/(dx)(e^(x))}sin +x^(3)e^(x){(d)/(dx)(sin x)}`
`=3x^(2)e^(x) sin x +x^(3)e^(x) sin x +x^(3) e^(x) cos x`
`=x^(2)e^(x)(3 sin x + x sin x + x cos x)`