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Popular >

derivative of ln(tanh(x))

Solution

\frac{d}{d x} (ln (tanh (x)))

Solution

sech^{2} (x) coth (x)

Solution steps

\frac{d}{d x} (ln (tanh (x)))

Apply the chain rule:

\frac{1}{tanh ( x )} \frac{d}{d x} (tanh (x))

= \frac{1}{tanh ( x )} \frac{d}{d x} (tanh (x))

\frac{d}{d x} (tanh (x)) = sech^{2} (x)

= \frac{1}{tanh ( x )} sech^{2} (x)

Simplify

\frac{1}{tanh ( x )} sech^{2} (x) : sech^{2} (x) coth (x)

= sech^{2} (x) coth (x)

Popular Examples

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\int 4 cos^{3} (5 x) d x

(\partial)/(\partial y)(2sin(y^2))

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x \to 5 lim (\frac{sin ( x )}{x})

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\int_{0}^{3} (x + 2) x + 1 d x

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\int \frac{x ^{14}}{x ^{5} - 1} d x

Frequently Asked Questions (FAQ)

What is the derivative of ln(tanh(x)) ?
The derivative of ln(tanh(x)) is sech^2(x)coth(x)
What is the first derivative of ln(tanh(x)) ?
The first derivative of ln(tanh(x)) is sech^2(x)coth(x)