Trouble finding the derivative of $\frac{4}{\sqrt{1-x}}$ I've been trying to figure out how to differentiate this expression, apparently I don't know my differentiation rules as much as I thought. I've been trying to use Wolfram Alpha as a guide but I'm at a loss.
I need to differentiate $$\frac{4}{\sqrt{1-x}}$$
I first pull out the four so the problem becomes: $$4 * \frac{1}{\sqrt{1-x}}$$
I'm not sure what to do next, do I use the quotient rule? Wolfram alpha is giving me some crazy answers, I would appreciate it if someone could walk me through this step by step. Thanks.

In this case (like many others), despite of you are working with a quotient, the quotient rule is not needed because you can rewrite your function in a convenient way as you can see below.
$$\begin{align*}\frac{d}{dx}\left[\frac{4}{\sqrt{1-x}}\right]&=4\frac{d}{dx}\left[\frac{1}{\sqrt{1-x}}\right]&\text{ (basic rule)}\\
\\
&=4\frac{d}{dx}\left[\frac{1}{(1-x)^{1/2}}\right]&\text{ (rewrite because it's convenient)}\\
&=4\frac{d}{dx}\left[(1-x)^{-1/2}\right]&\text{ (rewrite again)}\\
\\
&=4\left(-\frac{1}{2}(1-x)^{-3/2}\right)\cdot\frac{d}{dx}[1-x]&\text{ (chain rule)}\\
\\
&=-\frac{2}{(1-x)^{3/2}}\cdot(-1)&\text{ (rewrite + baisc rule)}\\
\\
&=\frac{2}{\sqrt{(1-x)^3}}&\text{ (rewrite)}\\
\end{align*}$$
