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

The answer to implicit (dy)/(dx),cos(x-y)=xe^x is (dy)/(dx)=-(-e^x-e^xx-sin(x-y))/(sin(x-y))

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

implicit derivative

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

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

Solution steps

cos (x - y) = x e^{x}

Treat

y

y (x)

Differentiate both sides:

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

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = - \frac{- e ^{x} - e ^{x} x - sin ( x - y )}{sin ( x - y )}

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

What is implicit (dy)/(dx),cos(x-y)=xe^x ?
The answer to implicit (dy)/(dx),cos(x-y)=xe^x is (dy)/(dx)=-(-e^x-e^xx-sin(x-y))/(sin(x-y))