Question

Find the derivative of f(x)=(lnx)^2. I know the answer, please show me the steps

Answer 1

\[\Large\bf\sf f(x)\quad=\quad (\ln x)^2\]We start by taking the derivative of the outermost function:\[\Large\bf\sf f'(x)\quad=\quad 2(\ln x)\cdot\color{royalblue}{(\ln x)'}\]The chain rule tells us to multiply by the derivative of the inner function.
That's where the blue term is coming from.
Taking it's derivative gives us:\[\Large\bf\sf f'(x)\quad=\quad 2(\ln x)\color{royalblue}{\frac{1}{x}}\]

Answer 2

The outermost function was (something)^2 which turned into 2(something).
Power rule.
I hope that step was clear.

Answer 3

ohhh! the chain rule! thank you sooo much