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}

f (x) = (4 x)^{l n (4 x)}

\int_{1}^{2} \frac{13}{x ^{3} + 3 x} d x

x \to \infty lim (2 x^{2} - 8)

x \to - 1 lim (\frac{3 - 1.1 + 1}{- 1.1 + 1})

\int \frac{( ln ( t ) ) ^{2}}{t} d t

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)