What is implicit (ex)/y =9x-y ?

The answer to implicit (ex)/y =9x-y is (dy)/(dx)=(9y^2-ey)/(-ex+y^2)

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implicit (ex)/y =9x-y

implicit derivative

\frac{e x}{y} = 9 x - y

\frac{d y}{d x} = \frac{9 y ^{2} - ey}{- e x + y ^{2}}

Solution steps

\frac{e x}{y} = 9 x - y

Treat

y

y (x)

Differentiate both sides:

\frac{e ( y - x \frac{d y}{d x} )}{y ^{2}} = 9 - \frac{d y}{d x}

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{9 y ^{2} - ey}{- e x + y ^{2}}

\frac{d y}{d x} = \frac{9 y ^{2} - ey}{- e x + y ^{2}}

\int \frac{17}{x ^{3} - 125} d x

(- 2, - 3), (6, 2)

\int \frac{sin ( x )}{e ^{x}} d x

\int \frac{1}{x 12 x + 25} d x

x \to 0 - lim (- x)

What is implicit (ex)/y =9x-y ?
The answer to implicit (ex)/y =9x-y is (dy)/(dx)=(9y^2-ey)/(-ex+y^2)