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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

implicit derivative

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

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

Solution steps

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

Treat

y

y (x)

Differentiate both sides:

\frac{e ^{\frac{x}{y}} ( y - x \frac{d y}{d x} )}{y ^{2}} = 1 - \frac{d y}{d x}

Isolate

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

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

y^{^{''}} + 16.67 y^{^{'}} + 10000 y = 0

y = 6 x^{2} - 6 x + 3, (1, 3)

\int 9 y d y

\int \frac{2}{3} x^{- \frac{1}{3}} d x

n \to 0 lim ((1 + n)^{\frac{1}{n}})

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