What is implicit (dy)/(dx),x^2-y^3=6 ?

The answer to implicit (dy)/(dx),x^2-y^3=6 is (dy)/(dx)=(2x)/(3y^2)

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implicit (dy)/(dx),x^2-y^3=6

implicit derivative

\frac{d y}{d x}, x^{2} - y^{3} = 6

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

Solution steps

x^{2} - y^{3} = 6

Treat

y

y (x)

Differentiate both sides:

2 x - 3 y^{2} \frac{d y}{d x} = 0

Isolate

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

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

What is implicit (dy)/(dx),x^2-y^3=6 ?
The answer to implicit (dy)/(dx),x^2-y^3=6 is (dy)/(dx)=(2x)/(3y^2)