If \(f(x)=x^2+2x\), then \(\dfrac{d}{dx}(f(\ln x))=\)

Summary Submit

We can use the chain rule:

$$\frac{d}{dx}[f(g(x))]=f'(g(x))\cdot g'(x) $$ $$ \frac{d}{dx}f(\ln x)= f'(\ln x)\cdot \frac{1}{x} $$ $$ f(x)=x^2+2x \hskip{2em} f'(x)=2x+2 \hskip{2em} f'(\ln x)= 2\ln x + 2$$ $$ \frac{d}{dx}f(\ln x) = \boxed{\frac{2\ln x+2}{x}} $$