What is implicit (dy)/(dx),50x^{1/3}y^{2/3}=600 ?

The answer to implicit (dy)/(dx),50x^{1/3}y^{2/3}=600 is (dy)/(dx)=-y/(2x)

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implicit (dy)/(dx),50x^{1/3}y^{2/3}=600

implicit derivative

\frac{d y}{d x}, 50 x^{\frac{1}{3}} y^{\frac{2}{3}} = 600

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

Solution steps

50 x^{\frac{1}{3}} y^{\frac{2}{3}} = 600

Treat

y

y (x)

Differentiate both sides:

\frac{50 ( 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}

What is implicit (dy)/(dx),50x^{1/3}y^{2/3}=600 ?
The answer to implicit (dy)/(dx),50x^{1/3}y^{2/3}=600 is (dy)/(dx)=-y/(2x)