# What is the implicit derivative of 2y^4-2xy-6x=-4 ?

Feb 24, 2016

$y ' = \frac{\left(2 y + 6\right)}{\left(8 {y}^{3} - 2 x\right)}$

#### Explanation:

$2 {y}^{4} - 2 x y - 6 x = - 4$

Differentiate both sides with respect to $x \Rightarrow$

$D \left(2 {y}^{4} - 2 x y - 6 x\right) = D \left(- 4\right)$

$8 {y}^{3.} y ' - 2 \left(x y ' + y\right) - 6 = 0$

$8 {y}^{3.} y ' - 2 x y ' - 2 y - 6 = 0$

$y ' \left(8 {y}^{3} - 2 x\right) = \left(2 y + 6\right)$

$y ' = \frac{\left(2 y + 6\right)}{\left(8 {y}^{3} - 2 x\right)}$