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

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

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

implicit derivative

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

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

Solution steps

x = e^{y}

Treat

y

y (x)

Differentiate both sides:

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

Isolate

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

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

\int \frac{5}{4 + 9 t ^{2}} d t

y^{3} - (18 x + 6) + 3 x y^{2} y^{^{'}} = 0

\int \frac{arctan ( x )}{x} d x

\frac{d}{d x} (6 x^{2} e^{- x})

y^{^{''}} + 4 y = 2 e^{x} + sin (2 x)

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