Question

Calcule aderivada implicita das equações x^3=sen(x)cos(y)

Answer 1

$x^3=\sin(x)\cos(y)\\\\3x^2=(\sin x)'(\cos y)+(\cos y)'(\sin x)\\3x^2=(\cos x)(\cos y)+(-y'\sin y)(\sin x)\\3x^2=\cos(x)\cos(y)-y'\sin(y)\sin(x)\\3x^2-\cos(x)\cos(y)=y'\sin(y)\sin(x)\\\\y'=\dfrac{3x^2-\cos(x)\cos(y)}{\sin(y)\sin(x)}$