Question

use implicit differentiation to find dy/dx if sinxy=5x+3y^2

Answer 1

is that sin(xy)?

Answer 2

Ooop, had to fix it: \[
\begin{array}{rcl}
\sin (xy)&=&5x+3y^2 \\
\frac{d}{dx} [ \sin (xy) ] &=& \frac{d}{dx} [ 5x+3y^2 ] \\
\cos (xy) \left(y+x\frac{dy}{dx}\right) &=& 5+6y \frac{dy}{dx} \\
y \cos (xy) + x\frac{dy}{dx} \cos (xy)\ &=& 5+6y \frac{dy}{dx} \\
x\frac{dy}{dx} \cos (xy)\ &=& 5+6y \frac{dy}{dx} -y \cos (xy) \\
x\frac{dy}{dx} \cos (xy)\ -6y \frac{dy}{dx} &=& 5-y \cos (xy) \\
(x\cos (xy)\ -6y) \frac{dy}{dx} &=& 5-y \cos (xy) \\
\frac{dy}{dx} &=& \frac{5-y \cos (xy)}{x\cos (xy)\ -6y}
\end{array}
\]

Answer 3

Thank you so much!