Question

Necesito encontrar la derivada implicita de esto
SEN ² (xy) + y COS(x)=2​

Answer 1

Hola !

$(\sin^2(xy)+y\cos(x) = 2)'\\\\2\sin(xy)\cos(xy)(y + x\cdot y') + y'\cos(x) - y\sin(x) = 0\\\\2y\sin(xy)\cos(xy)+2xy'\sin(xy)\cos(xy)+y'\cos(x)=y\sin(x)\\\\y'(2x\sin(xy)\cos(xy)+\cos(x)) = y(\sin(xy)-2\sin(xy)\cos(xy))\\\\y' = \frac{y(\sin(xy)-2\sin(xy)\cos(xy))}{2x\sin(xy)\cos(xy)+\cos(x)}$

Saludos ! :)