What is implicit (dy)/(dx),ysin(1/y)=1-xy ?

The answer to implicit (dy)/(dx),ysin(1/y)=1-xy is (dy)/(dx)=-(y^2)/(ysin(1/y)-cos(1/y)+xy)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

implicit (dy)/(dx),ysin(1/y)=1-xy

implicit derivative

\frac{d y}{d x}, y sin (\frac{1}{y}) = 1 - x y

\frac{d y}{d x} = - \frac{y ^{2}}{y sin ( \frac{1}{y} ) - cos ( \frac{1}{y} ) + x y}

Solution steps

y sin (\frac{1}{y}) = 1 - x y

Treat

y

y (x)

Differentiate both sides:

sin (\frac{1}{y}) \frac{d y}{d x} - \frac{cos ( \frac{1}{y} ) \frac{d y}{d x}}{y} = - x \frac{d y}{d x} - y

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = - \frac{y ^{2}}{y sin ( \frac{1}{y} ) - cos ( \frac{1}{y} ) + x y}

\frac{d y}{d x} = - \frac{y ^{2}}{y sin ( \frac{1}{y} ) - cos ( \frac{1}{y} ) + x y}

What is implicit (dy)/(dx),ysin(1/y)=1-xy ?
The answer to implicit (dy)/(dx),ysin(1/y)=1-xy is (dy)/(dx)=-(y^2)/(ysin(1/y)-cos(1/y)+xy)