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

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

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

implicit derivative

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

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

Solution steps

y^{3} = x

Treat

y

y (x)

Differentiate both sides:

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

Isolate

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

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

\int e^{- 3 x} x d x

y = \frac{x + 1}{x}

x \to - 1 - lim (\frac{2}{x + 1})

x \to - \infty lim (4 + \frac{3}{x})

\frac{\partial}{\partial x} (2 x^{y} + 8 y^{x} + 10)

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