How do you find the derivative of 4cosxsiny=1?

Sep 15, 2017

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{1}{4} \sec x \tan x \cos y$

Explanation:

We have, using identities:

$\sin y = \frac{1}{4 \cos x}$

$\sin y = \frac{1}{4} \sec x$

Using implicit differentiation/known derivative, we get:

$\cos y \left(\frac{\mathrm{dy}}{\mathrm{dx}}\right) = \frac{1}{4} \sec x \tan x$

Isolating the differential:

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{1}{4} \sec x \tan x \cos y$

Hopefully this helps!