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

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

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

implicit derivative

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

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

Solution steps

y^{2} = x

Treat

y

y (x)

Differentiate both sides:

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

Isolate

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

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

\frac{\partial}{\partial y} (4 x^{2} y^{2})

f (x) = 6 x

cos (x) (\frac{d y}{d x}) - sin (x) y = 0

x \to 1 lim (\frac{3}{x ^{2}})

\int x arctan (21 x) d x

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