# How do you differentiate f(x)=sinsqrtx using the chain rule?

Nov 24, 2015

$f ' \left(x\right) = \frac{\cos \sqrt{x}}{2 \sqrt{x}}$

#### Explanation:

According to the Chain Rule:

$f ' \left(x\right) = \cos \sqrt{x} \cdot {\overbrace{\frac{d}{\mathrm{dx}} \left[\sqrt{x}\right]}}^{\frac{d}{\mathrm{dx}} \left[{x}^{\frac{1}{2}}\right]}$

$f ' \left(x\right) = \cos \sqrt{x} \cdot \frac{1}{2} {x}^{- \frac{1}{2}}$

$f ' \left(x\right) = \frac{\cos \sqrt{x}}{2 \sqrt{x}}$