Question

Find the derivative in terms of x for 4sin(2y)cos(x)=2

Answer 1

I'm really struggling on this if someone could please help

Answer 2

\[4\sin(2y)\cos(x)=2 \implies \sin(2y) = \frac{1}{2\cos(x)} = \frac{1}{2}\sec(x)\]
\[\implies 2y = \sin^{-1}\left( \frac{1}{2}\sec(x) \right)\]
\[\implies y = \frac{1}{2}\sin^{-1}\left( \frac{1}{2}\sec(x) \right)\]

Answer 3

You could use the chain rule from here.

Answer 4

\[\frac{d}{dx}\left( \sin^{-1}x \right) = \frac{1}{\sqrt{1-x^2}}\]
\[\frac{d}{dx}\left( \sec x \right) = \sec x \tan x\]