How do you differentiate cos y +3x^2=6y?

Oct 16, 2016

I got: $\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{6 x}{6 + \sin \left(y\right)}$

Explanation:

Here we can use implicit differentiation including the term $\frac{\mathrm{dy}}{\mathrm{dx}}$ when differentiating $y$.

We get:

$- \sin \left(y\right) \frac{\mathrm{dy}}{\mathrm{dx}} + 6 x = 6 \frac{\mathrm{dy}}{\mathrm{dx}}$

we can collect $\frac{\mathrm{dy}}{\mathrm{dx}}$ on one side to get:

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{6 x}{6 + \sin \left(y\right)}$