# How do you find the derivative of y= 20x^(1/4) - 3x^(3/5) - 2e^x?

Apr 8, 2018

$\frac{\mathrm{dy}}{\mathrm{dx}} = 5 {x}^{- \frac{3}{4}} - \frac{9}{5} {x}^{- \frac{2}{5}} - 2 {e}^{x}$

#### Explanation:

$\text{differentiate using the "color(blue)"power rule}$

•color(white)(x)d/dx(ax^n)=nax^(n-1)

$\Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}} = 5 {x}^{\left(\frac{1}{4} - \frac{4}{4}\right)} - \frac{9}{5} {x}^{\left(\frac{3}{5} - \frac{5}{5}\right)} - 2 {e}^{x}$

$\textcolor{w h i t e}{\Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}}} = 5 {x}^{- \frac{3}{4}} - \frac{9}{5} {x}^{- \frac{2}{5}} - 2 {e}^{x}$