# How do you differentiate g(t)= 7/sqrt(t)?

Nov 15, 2016

$g ' \left(t\right) = \frac{- 7}{2 {t}^{\frac{3}{2}}}$

#### Explanation:

$g \left(t\right) = \frac{7}{\sqrt{t}}$

This can be solved multiple ways, such as using the quotient rule, or using the power rule. I prefer the power rule so I will rewrite $g \left(t\right)$:

$g \left(t\right) = \frac{7}{{t}^{\frac{1}{2}}}$
$g \left(t\right) = 7 {t}^{- \frac{1}{2}}$

Now to differentiate $g \left(t\right)$, use the power rule:

$g ' \left(t\right) = \left(- \frac{1}{2}\right) \left(7\right) \left({t}^{- \frac{3}{2}}\right)$
$g ' \left(t\right) = \left(- \frac{7}{2}\right) \left({t}^{- \frac{3}{2}}\right)$

$g ' \left(t\right) = \frac{- 7}{2 {t}^{\frac{3}{2}}}$