# Thread: use explicit differentiation to find y prime (simple)

1. ## use explicit differentiation to find y prime (simple)

$y = sin(3x+4y)$
$y' = cos(3x+4y)(3+4y')$
$\frac{y'}{3+4y'} = cos(3x+4y)$

2. ## Re: use explicit differentiation to find y prime (simple)

Hello, rabert1!

$y \:=\: \sin(3x+4y)$

$y' \:=\: \cos(3x+4y)\cdot (3+4y')$

We have: . . . . . . $y' \;=\;(3+4y')\cos(3x+4y)$

n . . . . . . . . . . . . $y' \;=\;3\cos(3x+4y) + 4y'\cos(3x+4y)$

. . . $y' - 4y'\cis(3x+4y) \;=\;3\cos(3x+4y)$ . .
Get the y' terms on one side.

$y'\big[1 - 4\cos(3x+4y)\big] \;=\;3\cos(3x+4y)$ . .
Factor.

w . . . . . . . . . . . . $y' \;=\;\frac{3\cos(3x+4y)}{1 - 4\cos(3x+4y)}$