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Popular >

derivative of ln(tanh(2x))

Solution

\frac{d}{d x} (ln (tanh (2 x)))

Solution

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

Solution steps

\frac{d}{d x} (ln (tanh (2 x)))

Apply the chain rule:

\frac{1}{tanh ( 2 x )} \frac{d}{d x} (tanh (2 x))

= \frac{1}{tanh ( 2 x )} \frac{d}{d x} (tanh (2 x))

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

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

Simplify

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

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

Popular Examples

y^{''}-3y^'-4y=10e^{-x}+4x+3

y^{^{''}} - 3 y^{^{'}} - 4 y = 10 e^{- x} + 4 x + 3

derivative of (5x-3(2x+5)^2)

\frac{d}{d x} ((5 x - 3) (2 x + 5)^{2})

derivative of (2x)/(9-tan(x))derivative of

\frac{2 x}{9 - tan ( x )}

limit as x approaches-4-of 1/(x+4)

x \to - 4 - lim (\frac{1}{x + 4})

y^{''}-10y^'+25y=0,y(0)=1,y(1)=0

y^{^{''}} - 10 y^{^{'}} + 25 y = 0, y (0) = 1, y (1) = 0

Frequently Asked Questions (FAQ)

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