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The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If $f(x)=ln\:a$ (where $a$ is a function of $x$), then $\displaystyle f'(x)=\frac{a'}{a}$

Learn how to solve differential calculus problems step by step online.

$\frac{1}{\mathrm{tanh}\left(\frac{x}{2}\right)}\frac{d}{dx}\left(\mathrm{tanh}\left(\frac{x}{2}\right)\right)$

Learn how to solve differential calculus problems step by step online. Find the derivative of ln(tanh(x/2)). The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If f(x)=ln\:a (where a is a function of x), then \displaystyle f'(x)=\frac{a'}{a}. Taking the derivative of hyperbolic tangent. The derivative of a function multiplied by a constant (\frac{1}{2}) is equal to the constant times the derivative of the function. Divide 1 by 2.

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