Question

How do you differentiate `sin3x^2`?

Answer 1

`6xcos3x^2`

Explanation:

differentiate using the `color(blue)"chain rule"`

`d/dx[f(g(x))]=f'(g(x)).g'(x)........ (A)`
`"------------------------------------------"`
`f(g(x))=sin3x^2rArrf'(g(x))=cos3x^2`

`g(x)=3x^2rArrg'(x)=6x`
`"--------------------------------------------"`
Substitute these values into (A)

`rArrd/dx[sin3x^2]=6xcos3x^2`