What is implicit (dy)/(dx),y^4=x^9 ?

The answer to implicit (dy)/(dx),y^4=x^9 is (dy)/(dx)=(9x^8)/(4y^3)

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implicit (dy)/(dx),y^4=x^9

implicit derivative

\frac{d y}{d x}, y^{4} = x^{9}

\frac{d y}{d x} = \frac{9 x ^{8}}{4 y ^{3}}

Solution steps

y^{4} = x^{9}

Treat

y

y (x)

Differentiate both sides:

4 y^{3} \frac{d y}{d x} = 9 x^{8}

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{9 x ^{8}}{4 y ^{3}}

\frac{d y}{d x} = \frac{9 x ^{8}}{4 y ^{3}}

\frac{d}{d x} (e^{x^{2} + 5 x})

(- 2.1) (- 1.7)

\int \frac{x ^{2}}{x ^{6} + 3 x ^{3} + 2} d x

x^{2} + 1, 3 - x

\frac{\partial}{\partial x} (\frac{e ^{x}}{y + x ^{5}})

What is implicit (dy)/(dx),y^4=x^9 ?
The answer to implicit (dy)/(dx),y^4=x^9 is (dy)/(dx)=(9x^8)/(4y^3)