# How do you implicitly differentiate  3x^2-y^2=7?

Nov 24, 2015

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{3 x}{y}$

#### Explanation:

When we implicitly differentiate with respect to $x$, we differentiate the $x$ terms like we normally would. However, when we reach a variable that's not $x$ (in this case, $y$), the chain rule kicks into effect and a $\frac{\mathrm{dy}}{\mathrm{dx}}$ term is spit out.

$\frac{d}{\mathrm{dx}} \left[3 {x}^{2} - {y}^{2} = 7\right]$

$6 x - 2 y \frac{\mathrm{dy}}{\mathrm{dx}} = 0$

$- 2 y \frac{\mathrm{dy}}{\mathrm{dx}} = - 6 x$

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{3 x}{y}$