What is implicit (dy)/(dx),sin(xy^3)=y^3 ?

The answer to implicit (dy)/(dx),sin(xy^3)=y^3 is (dy)/(dx)=-(ycos(xy^3))/(3(xcos(xy^3)-1))

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implicit (dy)/(dx),sin(xy^3)=y^3

implicit derivative

\frac{d y}{d x}, sin (x y^{3}) = y^{3}

\frac{d y}{d x} = - \frac{y cos ( x y ^{3} )}{3 ( x cos ( x y ^{3} ) - 1 )}

Solution steps

sin (x y^{3}) = y^{3}

Treat

y

y (x)

Differentiate both sides:

cos (x y^{3}) (y^{3} + 3 x y^{2} \frac{d y}{d x}) = 3 y^{2} \frac{d y}{d x}

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = - \frac{y cos ( x y ^{3} )}{3 ( x cos ( x y ^{3} ) - 1 )}

\frac{d y}{d x} = - \frac{y cos ( x y ^{3} )}{3 ( x cos ( x y ^{3} ) - 1 )}

What is implicit (dy)/(dx),sin(xy^3)=y^3 ?
The answer to implicit (dy)/(dx),sin(xy^3)=y^3 is (dy)/(dx)=-(ycos(xy^3))/(3(xcos(xy^3)-1))