# How do you differentiate y=-5^(4x^3)?

Jan 30, 2016

you have to use chain rule to differentiate this function. this is how you do it,

#### Explanation:

$\frac{\mathrm{dy}}{\mathrm{dx}}$
$= \frac{d}{\mathrm{dx}} \left(- {5}^{4 {x}^{3}}\right)$

$= - \frac{d}{\mathrm{dx}} \left({5}^{4 {x}^{3}}\right)$

suppose, a=5 so,

$- \frac{d}{\mathrm{dx}} \left({5}^{4 {x}^{3}}\right)$

$= - {5}^{4 {x}^{3}} \ln 5 \frac{d}{\mathrm{dx}} \left(4 {x}^{3}\right)$[as, $\frac{d}{\mathrm{dx}} \left({a}^{x}\right) = {a}^{x} \ln a$]

$= - {5}^{4 {x}^{3}} \ln 5 \cdot 4 \cdot 3 {x}^{2}$

$= - 12 \cdot {5}^{4 {x}^{3}} {x}^{2} \ln 5$