# What is the derivative of g(x)=sqrt(5-3x)?

Jul 5, 2016

$- \frac{3}{2 \sqrt{5 - 3 x}}$

#### Explanation:

The chain rule states:
d/dx(g(f(x)) = g'(f(x)) * f'(x)

In this example $g \left(x\right) = {\left(5 - 3 x\right)}^{\frac{1}{2}}$ $\to f \left(x\right) = 5 - 3 x$

Thus $\frac{d}{\mathrm{dx}} \left(g \left(x\right)\right) = \frac{1}{2} {\left(5 - 3 x\right)}^{- \frac{1}{2}} \cdot - 3$

$= - \frac{3}{2 \sqrt{5 - 3 x}}$