What is implicit y/(x-5y)=x^7+9 ?

The answer to implicit y/(x-5y)=x^7+9 is (dy}{dx}=\frac{7x^6(x-5y)^2+y)/x

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implicit y/(x-5y)=x^7+9

implicit derivative

\frac{y}{x - 5 y} = x^{7} + 9

\frac{d y}{d x} = \frac{7 x ^{6} ( x - 5 y ) ^{2} + y}{x}

Solution steps

\frac{y}{x - 5 y} = x^{7} + 9

Treat

y

y (x)

Differentiate both sides:

\frac{x \frac{d y}{d x} - y}{( x - 5 y ) ^{2}} = 7 x^{6}

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{7 x ^{6} ( x - 5 y ) ^{2} + y}{x}

\frac{d y}{d x} = \frac{7 x ^{6} ( x - 5 y ) ^{2} + y}{x}

x e^{y} \frac{d y}{d x} = 2 (e^{y} + x^{3} e^{2 x})

\frac{d y}{d x} = e^{5 x} + 10 y

\int_{0}^{1} \frac{1 + e ^{x}}{e ^{x}} d x

\frac{\partial}{\partial x} (\frac{- x - 6 y}{y ^{2} + 5 x ^{2}})

\frac{\partial}{\partial x} (2 - x^{2})

What is implicit y/(x-5y)=x^7+9 ?
The answer to implicit y/(x-5y)=x^7+9 is (dy}{dx}=\frac{7x^6(x-5y)^2+y)/x