# How do you find dy/dx by implicit differentiation given x^3=y^5?

Dec 11, 2016

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{3 {x}^{2}}{5 {y}^{4}}$

#### Explanation:

differentiate $\textcolor{b l u e}{\text{implicitly with respect to x}}$

differentiate both sides using the $\textcolor{b l u e}{\text{power rule}}$

$\Rightarrow 3 {x}^{2} = 5 {y}^{4.} \frac{\mathrm{dy}}{\mathrm{dx}}$

$\Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}} = \frac{3 {x}^{2}}{5 {y}^{4}}$