Question

If $y=\sqrt{a^2-x^2}$, find $\frac{dy}{dx}$

Answer 1

$\begin{array}{c}y=\sqrt{a^2-x^2}\\ \frac{dy}{dx}=\frac{d\sqrt{a^2-x^2}}{d\left(a^2-x^2\right)}\times \frac{d\left(a^2-x^2\right)}{dx}\\ =\frac{1}{2\sqrt{a^2-x^2}}\times -2x\\ =\frac{-x}{\sqrt{a^2-x^2}}\end{array}$