<s>[INST] Why is Implicit Differentiation needed for Derivative of $y = \arcsin (2x+1)$? my function is: $y = \arcsin (2x+1)$ and I want to find its derivative.
My approach was to apply the chain rule: 
$$y' = \frac{dg}{du} \frac{du}{dx}$$
with $g = \arcsin(u)$ and $u = 2x+1$. 
$$g' = \frac{1}{\sqrt{1-u^2}}.$$
${u}' = 2$. 
My solution therefore was
$$\frac{1}{\sqrt{1-u^2}} \cdot 2 = \frac{2}{\sqrt{1-(2x+1)^2}}.$$
This seems to be wrong and the correct solution is given by: 
$\frac{1}{\sqrt{-x^{2}-x}}$
I know that implicit differentiation should be used for this particular problem, but I do not really understand why. I appreciate any help!
 [/INST] $$\frac{2}{\sqrt{1-(1+2x)^2}}=\frac{2}{\sqrt{1-4x^2+
-4x-1}}=\frac{2}{\sqrt{-4x^2-4x}}=\frac{2}{\sqrt{4(-x^2-x)}}=\frac{2}{2\sqrt{-x^2-x}}=\frac{1}{\sqrt{-x^2-x}}$$
</s>