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Popular >

derivative of tanh(ln(x))

Solution

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

Solution

\frac{sech ^{2} ( ln ( x ) )}{x}

Solution steps

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

Apply the chain rule:

sech^{2} (ln (x)) \frac{d}{d x} (ln (x))

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

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

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

Simplify

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

= \frac{sech ^{2} ( ln ( x ) )}{x}

Popular Examples

integral of 1/(sqrt(x^2-a))

\int \frac{1}{x ^{2} - a} d x

derivative of e^{9x^2}+x

\frac{d}{d x} (e^{9 x^{2}} + x)

inverse oflaplace (3se^{-s})/(2s^2+8)inverse laplace

\frac{3 s e ^{- s}}{2 s ^{2} + 8}

limit as x approaches 2-of-2/(sqrt(2-x))

x \to 2 - lim (- \frac{2}{2 - x})

-2y^'+(4y)/x =x^4y^3

- 2 y^{^{'}} + \frac{4 y}{x} = x^{4} y^{3}

Frequently Asked Questions (FAQ)

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