# Implicit Diff with Cos

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• Sep 28th 2013, 10:36 AM
Jason76
Implicit Diff with Cos
$f(x) = y\cos(x) = 2x^{2} + 5y^{2}$

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

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

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

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

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

$y' = \dfrac{ \sin(x)y + 4x}{\cos(x) - 10y}$ :confused:
• Sep 28th 2013, 12:52 PM
HallsofIvy
Re: Implicit Diff with Cos
If your question is whether or not this is correct, yes, it is.