What is implicit (dy)/(dx),y=cos(x-y) ?

The answer to implicit (dy)/(dx),y=cos(x-y) is (dy)/(dx)=-(sin(x-y))/(1-sin(x-y))

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implicit (dy)/(dx),y=cos(x-y)

implicit derivative

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

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

Solution steps

y = cos (x - y)

Treat

y

y (x)

Differentiate both sides:

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

Isolate

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

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\frac{d}{d x} (\frac{x ^{2} + 2 x - 3}{( x + 1 ) ^{2}})

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What is implicit (dy)/(dx),y=cos(x-y) ?
The answer to implicit (dy)/(dx),y=cos(x-y) is (dy)/(dx)=-(sin(x-y))/(1-sin(x-y))