Derivera

Om jag har $g\left(x\right)=\left(f\right(x){)}^2$ och ska bestämma $g\text{'}\text{'}\left(x\right)$ detta korrekt? 

$$\begin{gathered} g\text{'}\left(x\right)=2f\left(x\right)f\text{'}\left(x\right) \\ g\text{'}\text{'}\left(x\right)=2f\text{'}\left(x\right)f\text{'}\left(x\right)+2f\left(x\right)f\text{'}\text{'}\left(x\right) \end{gathered}$$