# How do you differentiate y=(e^(5x^4))/(e^(4x^2+3))?

Nov 29, 2016

Rewrite as $y = {e}^{5 {x}^{4} - 4 {x}^{2} - 3}$, then use $\frac{d}{\mathrm{dx}} \left({e}^{u}\right) = {e}^{u} \frac{\mathrm{du}}{\mathrm{dx}}$

#### Explanation:

An important property of exponents is ${a}^{n} / {a}^{m} = {a}^{n - m}$

$y = {e}^{5 {x}^{4}} / {e}^{4 {x}^{2} + 3} = {e}^{5 {x}^{4} - 4 {x}^{2} - 3}$

$y ' = {e}^{5 {x}^{4} - 4 {x}^{2} - 3} \cdot \frac{d}{\mathrm{dx}} \left(5 {x}^{4} - 4 {x}^{2} - 3\right)$

$= \left(20 {x}^{3} - 8 x\right) {e}^{5 {x}^{4} - 4 {x}^{2} - 3}$