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

The answer to implicit (dy)/(dx),y^4=4xy is (dy)/(dx)= y/(y^3-x)

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

implicit derivative

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

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

Solution steps

y^{4} = 4 x y

Treat

y

y (x)

Differentiate both sides:

4 y^{3} \frac{d y}{d x} = 4 (y + x \frac{d y}{d x})

Isolate

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

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

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\int - 3 csc (x) cot (x) d x

f (x) (6 x^{2} - 3) (1. 5^{x})

\frac{\partial}{\partial x} (y^{6} sin (3 x))

What is implicit (dy)/(dx),y^4=4xy ?
The answer to implicit (dy)/(dx),y^4=4xy is (dy)/(dx)= y/(y^3-x)