What is implicit (dy)/(dx),e^{x/y}=7x-y ?

The answer to implicit (dy)/(dx),e^{x/y}=7x-y is (dy)/(dx)=(7y^2-e^{x/y}y)/(-e^{x/y)x+y^2}

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implicit (dy)/(dx),e^{x/y}=7x-y

implicit derivative

\frac{d y}{d x}, e^{\frac{x}{y}} = 7 x - y

\frac{d y}{d x} = \frac{7 y ^{2} - e ^{\frac{x}{y}} y}{- e ^{\frac{x}{y}} x + y ^{2}}

Solution steps

e^{\frac{x}{y}} = 7 x - y

Treat

y

y (x)

Differentiate both sides:

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

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{7 y ^{2} - e ^{\frac{x}{y}} y}{- e ^{\frac{x}{y}} x + y ^{2}}

\frac{d y}{d x} = \frac{7 y ^{2} - e ^{\frac{x}{y}} y}{- e ^{\frac{x}{y}} x + y ^{2}}

x y^{^{'}} - 2 y = x

n = 0 \sum \infty \frac{n 2 ^{n}}{3 ^{n}}

y = x^{3} (2 x - 1)^{5}

\frac{\partial}{\partial x} (\frac{x + y}{1 - x y})

f (x) = x^{3} - 3 x

What is implicit (dy)/(dx),e^{x/y}=7x-y ?
The answer to implicit (dy)/(dx),e^{x/y}=7x-y is (dy)/(dx)=(7y^2-e^{x/y}y)/(-e^{x/y)x+y^2}