# How do you find the derivative of g(x)=sqrt(5-3x)?

Apr 22, 2015

Let h(x) = x^(1/2) and k(x) = 5-3x#

so $g \left(x\right) = \sqrt{5 - 3 x} = h \left(k \left(x\right)\right)$

$\frac{d g \left(x\right)}{\mathrm{dx}} = \frac{d h \left(k \left(x\right)\right)}{d k \left(x\right)} \cdot \frac{d k \left(x\right)}{\mathrm{dx}}$

$= \left(\frac{1}{2}\right) {\left(k \left(x\right)\right)}^{- \frac{1}{2}} \cdot \left(- 3\right)$

$= \left(- \frac{3}{2}\right) \cdot \frac{1}{\sqrt{5 - 3 x}}$

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