Derivative of sum of two functions I have to find $\frac{dy}{dx}\left[(x\sqrt{x})+\frac{1}{x^2\sqrt{x}}\right]$ but would like to find where I made a mistake in my solution.
Here is my work:
\begin{align} 
(f+g)'=& \ f'+g', f = x \sqrt{x}, g= \frac{1}{x^2 \sqrt x}\\ f=& \ x \cdot x^{1/2} = x^{3/2} 
\\ f'=& \  \frac{3}{2x\sqrt{x}} \\ \\ 
g =& \ x^{-2}\cdot x^{-1/2} \\ g =& \ x^{-5/2} \\ g' =& \ -\frac{5}{2x^3 \sqrt{x}} \\ \\ f'+g' =& \ \frac{3}{2x\sqrt{x}} - \frac{5}{2x^3 \sqrt{x}} \\ =& \ \frac{3x^2-5}{2x^3 \sqrt x} \\ \frac{dy}{dx}=& \ \frac{\sqrt x (3x^2-5)}{2x^4}
\end{align}

In general if $f(x)=x^{n}$ for some constant $n$ then $f'(x)=nx^{n-1}$ which is the power rule.
