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Popular >

derivative of ln(1-e^{-x})

Solution

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

Solution

\frac{e ^{- x}}{1 - e ^{- x}}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{1 - e ^{- x}} e^{- x} : \frac{e ^{- x}}{1 - e ^{- x}}

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

Popular Examples

sum from n=1 to infinity of 1/(2^n-5)

n = 1 \sum \infty \frac{1}{2 ^{n} - 5}

(dy)/(dt)+0.7ty=7t

\frac{d y}{d t} + 0.7 t y = 7 t

normal of y=5x^2+2xy-3y^2+3,(2,1)normal of

y = 5 x^{2} + 2 x y - 3 y^{2} + 3, (2, 1)

(\partial)/(\partial x)(1-9x^2-6y^2)

\frac{\partial}{\partial x} (1 - 9 x^{2} - 6 y^{2})

derivative of f(x)=(x+2)*sqrt(-x)derivative of

f (x) = (x + 2) \cdot - x

Frequently Asked Questions (FAQ)

What is the derivative of ln(1-e^{-x}) ?
The derivative of ln(1-e^{-x}) is (e^{-x})/(1-e^{-x)}
What is the first derivative of ln(1-e^{-x}) ?
The first derivative of ln(1-e^{-x}) is (e^{-x})/(1-e^{-x)}