If , determine .
2^(1/2) but it wrongs
5lnx/x but it wrongs
help?
To calculate these derivatives we use the Power Rule and the Chain Rule:
$\displaystyle \begin{aligned}
\frac{d}{dx}x^n&=nx^{n-1}\\
\frac{d}{dx}f(g(x))&=f'(g(x))g'(x).
\end{aligned}$
For example,
$\displaystyle \frac{d}{dx}(\ln x)^5=5(\ln x)^4\frac{d}{dx}\ln x.$