How do you find the derivative of sqrt(9-x)?

Mar 10, 2016

-1/(2sqrt(9-x)

Explanation:

differentiate using the$\textcolor{b l u e}{\text{ chain rule }}$

$\frac{d}{\mathrm{dx}} \left[f \left(g \left(x\right)\right)\right] = f ' \left(g \left(x\right)\right) . g ' \left(x\right)$

now $\sqrt{9 - x} = {\left(9 - x\right)}^{\frac{1}{2}}$

$\Rightarrow \frac{d}{\mathrm{dx}} {\left(9 - x\right)}^{\frac{1}{2}} = \frac{1}{2} {\left(9 - x\right)}^{- \frac{1}{2}} . \frac{d}{\mathrm{dx}} \left(9 - x\right)$

$= - \frac{1}{2 \sqrt{9 - x}}$