Question

How do you differentiate `3sin^2(3x)` using the chain rule?

Answer 1

`18sin(3x)cos(3x)`

Explanation:

chain rule for 3 functions is `d/dx(f(g(h(x))))=f'(g(h(x)))*d/dx(g(h(x)))=f'(g(h(x)))g'(h(x))h'(x)`

in this problem, `f(x)=3x^2`, `g(x)=sin(x)`, and `h(x)=3x`
that means: `f'(x)=6x`, `g'(x)=cos(x)`, and `h(x)=3`

so `d/dx(3sin^2(3x))=6(sin(3x))*cos(3x)*3`
`=18sin(3x)cos(3x)`