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

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

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

implicit derivative

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

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

Solution steps

x = y e^{y}

Treat

y

y (x)

Differentiate both sides:

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

Isolate

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

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

n = 1 \sum \infty 3 (- \frac{2}{3})^{n}

\frac{d y}{d x} = \frac{2 + y ^{2}}{2 x y}, y (1) = 1

\int x x^{2} + 3 d x

\int \frac{x}{- x ^{2} + 5} d x

\int_{0}^{\frac{3}{2}} x cos (π x) d x

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