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

The answer to implicit (dy)/(dx),y^4=2x is (dy)/(dx)= 1/(2y^3)

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implicit (dy)/(dx),y^4=2x

implicit derivative

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

\frac{d y}{d x} = \frac{1}{2 y ^{3}}

Solution steps

y^{4} = 2 x

Treat

y

y (x)

Differentiate both sides:

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

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{1}{2 y ^{3}}

\frac{d y}{d x} = \frac{1}{2 y ^{3}}

\int_{0}^{\infty} x y e^{- y x} d x

\frac{14}{2 x + 16}

x y^{3} d y = d x, y (1) = 2

\int \frac{x ^{3} - 3 x ^{2} + 2 x - 4}{x - 1} d x

x \to 0 lim (\frac{e ^{x} - 1}{11 x})

What is implicit (dy)/(dx),y^4=2x ?
The answer to implicit (dy)/(dx),y^4=2x is (dy)/(dx)= 1/(2y^3)