# Math Help - Implicit Diff with Cos

1. ## Implicit Diff with Cos

$f(x) = y\cos(x) = 2x^{2} + 5y^{2}$

$[\cos(x)][1]y' + [y][-\sin(x)] = 4x + 10yy'$

$\cos(x)y' + [-\sin(x)y] = 4x + 10yy'$

$\cos(x)y' - \sin(x)y = 4x + 10yy'$

$\cos(x)y' - 10yy' = \sin(x)y + 4x$

$y'[\cos(x) - 10y] = \sin(x)y + 4x$

$y' = \dfrac{ \sin(x)y + 4x}{\cos(x) - 10y}$

2. ## Re: Implicit Diff with Cos

If your question is whether or not this is correct, yes, it is.