What is implicit (dy)/(dx),y^3=4x ?

The answer to implicit (dy)/(dx),y^3=4x is (dy)/(dx)= 4/(3y^2)

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implicit (dy)/(dx),y^3=4x

implicit derivative

\frac{d y}{d x}, y^{3} = 4 x

\frac{d y}{d x} = \frac{4}{3 y ^{2}}

Solution steps

y^{3} = 4 x

Treat

y

y (x)

Differentiate both sides:

3 y^{2} \frac{d y}{d x} = 4

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{4}{3 y ^{2}}

\frac{d y}{d x} = \frac{4}{3 y ^{2}}

\int (y ln (y)) d y

\frac{\partial}{\partial x} ((x y - 3) e^{- x y})

\frac{\partial}{\partial x} (\frac{- 3 x}{x ^{2} + y ^{2}})

\int \frac{1}{x ^{2} + b} d x

\int_{- 8}^{32} \frac{1}{∣ 2 x ∣} d x

What is implicit (dy)/(dx),y^3=4x ?
The answer to implicit (dy)/(dx),y^3=4x is (dy)/(dx)= 4/(3y^2)