What is implicit (dy)/(dx),40x^{1/3}y^{2/3}=480 ?

The answer to implicit (dy)/(dx),40x^{1/3}y^{2/3}=480 is (dy)/(dx)=-y/(2x)

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implicit (dy)/(dx),40x^{1/3}y^{2/3}=480

implicit derivative

\frac{d y}{d x}, 40 x^{\frac{1}{3}} y^{\frac{2}{3}} = 480

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

Solution steps

40 x^{\frac{1}{3}} y^{\frac{2}{3}} = 480

Treat

y

y (x)

Differentiate both sides:

\frac{40 ( y + 2 x \frac{d y}{d x} )}{3 x ^{\frac{2}{3}} y ^{\frac{1}{3}}} = 0

Isolate

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

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

\int \frac{2 x}{( x - 1 ) ( x - 2 )} d x

\int \frac{( x ^{2} + 3 x + 1 )}{x} d x

\frac{d}{d x} (\frac{4 y ^{2} - x ^{4}}{4 x y})

\int \frac{2 x}{x ^{2} - 49} d x

ln (3 - x), 2

What is implicit (dy)/(dx),40x^{1/3}y^{2/3}=480 ?
The answer to implicit (dy)/(dx),40x^{1/3}y^{2/3}=480 is (dy)/(dx)=-y/(2x)