Question

How do you differentiate `y=[x(x+sin^2x)^3]^4`?

Answer 1

`y'=4x^3(x+sin^2(x))^12+12x^4(x+sin^2(x))^11(1+sin(2x))`

Explanation:

Using the product rule we have
`y'=f'g+fg'`
so we get for the first summand `4x^3`
and for the second one
`12(x+sin^2(x))^11*(1+2sin(x)cos(x))`
Now use that
`sin(2x)=2sin(x)cos(x)`