# How do you find the derivative of x^2+y^2=e^(3x)?

May 12, 2016

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{3 {e}^{3 x} - 2 x}{2 y}$

#### Explanation:

Here we use the concept of function of a function and whenever we consider derivative w.r.t. $y$, we multiply by $\frac{\mathrm{dy}}{\mathrm{dx}}$.

Hence taking derivative of both sides in ${x}^{2} + {y}^{2} = {e}^{3 x}$

$2 x + 2 y \frac{\mathrm{dy}}{\mathrm{dx}} = {e}^{3 x} \cdot 3$

or $\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{3 {e}^{3 x} - 2 x}{2 y}$