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

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

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

implicit derivative

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

\frac{d y}{d x} = \frac{1}{4 y ^{3}}

Solution steps

x = y^{4}

Treat

y

y (x)

Differentiate both sides:

1 = 4 y^{3} \frac{d y}{d x}

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{1}{4 y ^{3}}

\frac{d y}{d x} = \frac{1}{4 y ^{3}}

y^{^{'}} - \frac{6}{x} y = x^{9} y^{8}

\int - \frac{1}{csc ( y )} d y

\frac{d}{d x} (cos^{2} (ln (x + 1)) - e^{x^{2}})

y = 5 x - 1

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