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)

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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}

\frac{\partial}{\partial y} (x y e^{x})

\int x - x^{3} d x

\int (1 + 4 x)^{3} d x

\frac{d}{d x} (lo g_{8} (x))

\int cot^{6} (2 t) d t

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)