Question

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

Answer 1

`(2x)/(x^2 + 2 )`

Explanation:

Chain rule: `d/dx f(g(x) ) = f'(g(x)) g'(x)`

`=> d/dx ln f(x) =( f'(x))/f(x)`

`=> d/dx ln(x^2 + 2) = (d/dx(x^2+2)) / (x^2 + 2)`

`therefore = (2x)/(x^2 + 2 )`