Differentiate the functions with respect to x`cosx^3dotsin^2(x^5)`

Explanation

Let `y cos x^(3) . sin ^(2) (x^(5)) `
`rArr (dy)/(dx)=(d)/(dx) [cos x ^(3) . sin ^(2) (x^(2))]`
=` cos x ^(3) .(d)/(dx) sin^(2) (x^(5)) +sin^(2)(x^(5))(d)/(dx)cos x^(3)`
`= cos x ^(3) . 2 sin (x^(5)) + sin (x^(5))`
`+ sin ^(2) (x^(5))(-sin x^(3))(d)/(dx) x^(3)`
`= cos ^(3) . 2sin (x^(5)) cos (x^(5)).(d)/(dx) x ^(5)`
` - 3 x^(2) sin ^(2) (x^(5)) sin x^(3)`
`= 5x^(4) cos x^(3). sin (2x^(5))`
` - 3 x^(2) sin ^(2) (x^(5)) sin x^(3)`