# How do you find (dy)/(dx) given y^4=100x?

Apr 16, 2017

#### Explanation:

Implicitly differentiate: ${y}^{4} = 100 x$:

$4 {y}^{3} \frac{\mathrm{dy}}{\mathrm{dx}} = 100$

Divide both sides by $4 {y}^{3}$:

$\frac{\mathrm{dy}}{\mathrm{dx}} = 25 {y}^{-} 3$

If you do not want to leave it like this, then you would have been better off solving for y and then differentiating as follows:

$y = \sqrt{10} {x}^{\frac{1}{4}}$

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{\sqrt{10}}{4} {x}^{- \frac{3}{4}}$