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

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

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implicit (dy)/(dx),xy^2=4

implicit derivative

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

\frac{d y}{d x} = - \frac{y}{2 x}

Solution steps

x y^{2} = 4

Treat

y

y (x)

Differentiate both sides:

y^{2} + 2 x y \frac{d y}{d x} = 0

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = - \frac{y}{2 x}

\frac{d y}{d x} = - \frac{y}{2 x}

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