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

The answer to implicit (dy)/(dx),2x=y^4 is (dy)/(dx)= 1/(2y^3)

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implicit (dy)/(dx),2x=y^4

implicit derivative

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

\frac{d y}{d x} = \frac{1}{2 y ^{3}}

Solution steps

2 x = y^{4}

Treat

y

y (x)

Differentiate both sides:

2 = 4 y^{3} \frac{d y}{d x}

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{1}{2 y ^{3}}

\frac{d y}{d x} = \frac{1}{2 y ^{3}}

x \to 0 lim (\frac{x}{- 4 x ^{3} - 8 x})

\frac{\partial}{\partial t} (\frac{( s - 3 r )}{t})

\int 2 x (x^{2} + 1)^{4} d x

\int 1 + x^{2} x^{5} d x

5 + x e^{3 x}

What is implicit (dy)/(dx),2x=y^4 ?
The answer to implicit (dy)/(dx),2x=y^4 is (dy)/(dx)= 1/(2y^3)