Question

How do you differentiate `f(x)=ln (x^3+3)`?

Answer 1

`f'(x) = (3x^2)/(x^3+3)`

Explanation:

`f(x) = ln(x^3+3)`

To differentiate we use the chain rule:
`d/dxf(g(x)) =f'(g(x))g'(x)` or,`dy/dx=dy/(du)(du)/dx`

`:. f'(x) = 1/(x^3+3) d/dx(x^3+3)`

`:. f'(x) = 1/(x^3+3)(3x^2)`

`:. f'(x) = (3x^2)/(x^3+3)`