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

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

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implicit (dy)/(dx),y^2=x^3

implicit derivative

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

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

Solution steps

y^{2} = x^{3}

Treat

y

y (x)

Differentiate both sides:

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

Isolate

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

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

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