Question

How do you find the derivative of `(ln(x^(2)+3))^(3)`?

Answer 1

`(df)/(dx)=(6x(ln(x^2+3))^2)/(x^2+3)`

Explanation:

Here `f(x)=(g(x))^3`, where `g(x)=ln(h(x))` and `h(x)=x^2+3`

According to chain rule `(df)/(dx)=(df)/(dg)xx(dg)/(dh)xx(dh)/(dx)`

Hence `(df)/(dx)=3(ln(x^2+3))^2xx1/(x^2+3)xx2x`

= `(6x(ln(x^2+3))^2)/(x^2+3)`