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Popular >

derivative of ln((e^x/(e^x-1)))

Solution

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

Solution

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

Solution steps

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

Simplify

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

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d x}{d x} = 1

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

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

Popular Examples

tangent of f(x)=sqrt(x-1),\at x=10 tangent of

f (x) = x - 1, at x = 10

derivative of (e^x)/(e^x-e^{-x)}derivative of

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

((dy)/(dx))+2y=e^{-x}

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

derivative of (x^2/(x^2+x+2))

\frac{d}{d x} (\frac{x ^{2}}{x ^{2} + x + 2})

(\partial)/(\partial y)(e^x-1)

\frac{\partial}{\partial y} (e^{x} - 1)

Frequently Asked Questions (FAQ)

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