Question

Calcule aderivada implicita das equações x=sen(xy^2)

Answer 1

$x=\sin(xy^2)\\\\u=xy^2\\u'=(x)'(y^2)+(x)(y^2)'\\u'=y^2+2xyy'\\\\1=(y^2+2xyy')(\cos(xy^2))\\1=y^2\cos(xy^2)+2xyy'\cos(xy^2)\\2xyy'\cos(xy^2)=1-y^2\cos(xy^2)\\\\y'=\dfrac{1-y^2\cos(xy^2)}{2xy\cos(xy^2)}$