What is implicit (dy)/(dx),y^5=x^7 ?

The answer to implicit (dy)/(dx),y^5=x^7 is (dy)/(dx)=(7x^6)/(5y^4)

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implicit (dy)/(dx),y^5=x^7

implicit derivative

\frac{d y}{d x}, y^{5} = x^{7}

\frac{d y}{d x} = \frac{7 x ^{6}}{5 y ^{4}}

Solution steps

y^{5} = x^{7}

Treat

y

y (x)

Differentiate both sides:

5 y^{4} \frac{d y}{d x} = 7 x^{6}

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{7 x ^{6}}{5 y ^{4}}

\frac{d y}{d x} = \frac{7 x ^{6}}{5 y ^{4}}

x^{2} + 3 x + \frac{1}{x ^{2}}

\int \frac{arcsin ( 4 x )}{1 - 16 x ^{2}} d x

\frac{x ^{2}}{7 + x}

\frac{d}{d x} (x (3 x + 5)^{3})

What is implicit (dy)/(dx),y^5=x^7 ?
The answer to implicit (dy)/(dx),y^5=x^7 is (dy)/(dx)=(7x^6)/(5y^4)