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 )}

\int \frac{1 - x ^{2}}{4} d x

cos^{3} (x), at x = 0

\frac{2 x ^{3}}{3} - 12 x

\frac{d}{d x} (\frac{x ^{2}}{x + 5})

f (x) = 5 x^{4}

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))