What is implicit (dy)/(dx),e^{x/y}=4x-y ?

The answer to implicit (dy)/(dx),e^{x/y}=4x-y is (dy)/(dx)=(4y^2-e^{x/y}y)/(-e^{x/y)x+y^2}

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implicit (dy)/(dx),e^{x/y}=4x-y

implicit derivative

\frac{d y}{d x}, e^{\frac{x}{y}} = 4 x - y

\frac{d y}{d x} = \frac{4 y ^{2} - e ^{\frac{x}{y}} y}{- e ^{\frac{x}{y}} x + y ^{2}}

Solution steps

e^{\frac{x}{y}} = 4 x - y

Treat

y

y (x)

Differentiate both sides:

\frac{e ^{\frac{x}{y}} ( y - x \frac{d y}{d x} )}{y ^{2}} = 4 - \frac{d y}{d x}

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{4 y ^{2} - e ^{\frac{x}{y}} y}{- e ^{\frac{x}{y}} x + y ^{2}}

\frac{d y}{d x} = \frac{4 y ^{2} - e ^{\frac{x}{y}} y}{- e ^{\frac{x}{y}} x + y ^{2}}

\int_{0}^{4} (2 - x)^{2} d x

n = 0 \sum \infty \frac{1}{n + 14}

\int t + 2 + \frac{3}{t ^{2} + 1} d t

\frac{d}{d x} (\frac{- 8 x ^{7} + 7 x ^{3} - 2}{- 4 x ^{3}})

\int (a x + b + x^{2})^{2} d x

What is implicit (dy)/(dx),e^{x/y}=4x-y ?
The answer to implicit (dy)/(dx),e^{x/y}=4x-y is (dy)/(dx)=(4y^2-e^{x/y}y)/(-e^{x/y)x+y^2}