What is the derivative of ln(2-e^x) ?

The derivative of ln(2-e^x) is -(e^x)/(2-e^x)

What is the first derivative of ln(2-e^x) ?

The first derivative of ln(2-e^x) is -(e^x)/(2-e^x)

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derivative of

ln (2 - e^{x})

- \frac{e ^{x}}{2 - e ^{x}}

Solution steps

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

Apply the chain rule:

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

= \frac{1}{2 - e ^{x}} \frac{d}{d x} (2 - e^{x})

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

= \frac{1}{2 - e ^{x}} (- e^{x})

Simplify

\frac{1}{2 - e ^{x}} (- e^{x}) : - \frac{e ^{x}}{2 - e ^{x}}

= - \frac{e ^{x}}{2 - e ^{x}}

x \to (1 + 1) lim (\frac{1}{x - 2})

y^{^{''}} + 5 y = 0

\int \frac{7 x + 2}{x ^{2} + x} d x

\int \frac{1}{x 324 - x ^{2}} d x

3^{9 x}

What is the derivative of ln(2-e^x) ?
The derivative of ln(2-e^x) is -(e^x)/(2-e^x)
What is the first derivative of ln(2-e^x) ?
The first derivative of ln(2-e^x) is -(e^x)/(2-e^x)