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Popular >

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

Solution

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

Solution

\frac{e ^{2 x} + 1}{e ^{2 x} - 1}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{e ^{2 x} + 1}{e ^{2 x} - 1}

Popular Examples

derivative of (x^3+2x+3/(x^2))

\frac{d}{d x} (\frac{x ^{3} + 2 x + 3}{x ^{2}})

integral of y/(sqrt(16+y^2))

\int \frac{y}{16 + y ^{2}} d y

x^5+y^4sqrt(x^6+4)y^'=0

x^{5} + y^{4} x^{6} + 4 y^{^{'}} = 0

(\partial)/(\partial x)(-6e^xcos(yz))

\frac{\partial}{\partial x} (- 6 e^{x} cos (yz))

limit as x approaches 1 of (x^4-6x^2+8x-3)/(x^4-2x^3+2x-1)

x \to 1 lim (\frac{x ^{4} - 6 x ^{2} + 8 x - 3}{x ^{4} - 2 x ^{3} + 2 x - 1})

Frequently Asked Questions (FAQ)

What is the derivative of ln(e^x-e^{-x}) ?
The derivative of ln(e^x-e^{-x}) is (e^{2x}+1)/(e^{2x)-1}
What is the first derivative of ln(e^x-e^{-x}) ?
The first derivative of ln(e^x-e^{-x}) is (e^{2x}+1)/(e^{2x)-1}