Question: I am stuck on an exercise where I have to figure out the derivative of $y = \frac{\sqrt{20-x^2}}{4}$. I realize that this equation can be rewritten as:

$1/4 \* \sqrt{20-x^2}$, so when I factor out the constant 1/4 on beforehand, this leaves me with $\sqrt{20-x^2}$. This can be rewritten as a power $(20-x^2)^{0.5}$. 

My idea was to simply apply the power rule to this equation to find the derivative. This leads to:

$0.5(20-x^2)^{-0.5} = \frac{1}{2} \* \frac{1}{\sqrt{20-x^2}} = \frac{1}{2\sqrt{20-x^2}}$

However my solution is not valid, and wolfram alpha does something complicated using the chain rule instead. Please help me understand why.

Answer: 
You can employ the power rule, but you forget that in doing so, you're also invoking the chain rule, with kernel $(20-x^2)$. That means you have to multiply your result with the derivative of this expression as well, which is $-2x$. That should give you the answer you're after. Also, don't forget to put back the $\frac{1}{4}$-factor you stripped away at the beginning.
You should multiply also by the derivative of $(20-x^2)$, which is equal to $-2x$. Let's try this.