What is implicit (dy)/(dx),e^{(x/y)}=6x-y ?

The answer to implicit (dy)/(dx),e^{(x/y)}=6x-y is (dy)/(dx)=(6y^2-e^{x/y}y)/(-e^{x/y)x+y^2}

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implicit (dy)/(dx),e^{(x/y)}=6x-y

implicit derivative

\frac{d y}{d x}, e^{(\frac{x}{y})} = 6 x - y

\frac{d y}{d x} = \frac{6 y ^{2} - e ^{\frac{x}{y}} y}{- e ^{\frac{x}{y}} x + y ^{2}}

Solution steps

e^{\frac{x}{y}} = 6 x - y

Treat

y

y (x)

Differentiate both sides:

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

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{6 y ^{2} - e ^{\frac{x}{y}} y}{- e ^{\frac{x}{y}} x + y ^{2}}

\frac{d y}{d x} = \frac{6 y ^{2} - e ^{\frac{x}{y}} y}{- e ^{\frac{x}{y}} x + y ^{2}}

(x - 2) (x^{2} - 10 x + 25)

\frac{d x}{d y} = 4 (x^{2} 1), x (\frac{π}{4}) = 1

(3 x^{2} + y - 4) - (2 y - x) \cdot \frac{d y}{d x} = 0

(x + 1)^{2} (x^{2} + 1)^{- 3}

\frac{d y}{d x} - \frac{y}{x} = - \frac{5}{2} x^{2} y^{3}

What is implicit (dy)/(dx),e^{(x/y)}=6x-y ?
The answer to implicit (dy)/(dx),e^{(x/y)}=6x-y is (dy)/(dx)=(6y^2-e^{x/y}y)/(-e^{x/y)x+y^2}