What is implicit (dy)/(dx),ye^x=y ?

The answer to implicit (dy)/(dx),ye^x=y is (dy)/(dx)=-(e^xy)/(e^x-1)

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implicit (dy)/(dx),ye^x=y

implicit derivative

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

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

Solution steps

y e^{x} = y

Treat

y

y (x)

Differentiate both sides:

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

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = - \frac{e ^{x} y}{e ^{x} - 1}

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

\frac{d}{d x} ((3 x + 1) \frac{( x ^{2} + 4 )}{( 6 x - 5 )})

\int \frac{sin ( 2 x )}{sin ( x )} d x

y = 2 csc (8 x^{3} - 8 x + 8)

\int_{0}^{1} 8 cos (4 x) d x

\int tan^{3} (x) sec^{5} (x) d x

What is implicit (dy)/(dx),ye^x=y ?
The answer to implicit (dy)/(dx),ye^x=y is (dy)/(dx)=-(e^xy)/(e^x-1)