Question

If `f(x)= cos3x` and `g(x) = sqrt(x+3`, how do you differentiate `f(g(x))` using the chain rule?

Answer 1

`(d(f@g)(x))/dx=-3/(2sqrt(x+3))sin(3sqrt(x+3))`

Explanation:

The composition function `(f@g)(x)` is found as follows :

`f[g(x)]=f(sqrt(x+3))`

`=cos(3sqrt(x+3))`

`therefore(d(f@g)(x))/dx=d/dxcos(3sqrt(x+3))`

`=-sin(3sqrt(x+3))*3/2(x+3)^(-1/2)(1)`

`=-3/(2sqrt(x+3))sin(3sqrt(x+3))`