Question

How do you differentiate `f(x)=e^(((ln(x^2+3))^2)` using the chain rule.?

Answer 1

`e^((ln(x^2+3))^2)*4x(ln(x^2+3)/(x^2+3))`

Explanation:

first find the derivative of `((ln(x^2+3))^2)`, the expression in the power of e then multiply it with `e^((ln(x^2+3))^2)`

Answer 2

Set `u(x)=(ln(x^2+3))^2` hence

`((df)/dx)=e^(u(x))*((du)/dx)`

where

`(du)/dx=[4xln(x^2+3)]/[x^2+3]`