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Popular >

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

Solution

derivative of

y = 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-4x^2-7x tangent of

- 4 x^{2} - 7 x

derivative of f(4)=10x-13 derivative of

f (4) = 10 x - 13

derivative of xe^{rx}

\frac{d}{d x} (x e^{r x})

x^2y^{''}+2xy^'-2y=0

x^{2} y^{^{''}} + 2 x y^{^{'}} - 2 y = 0

tangent of f(x)=9e^x12x,\at x=0 tangent of

f (x) = 9 e^{x} 12 x, at x = 0

Frequently Asked Questions (FAQ)

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