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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 $\displaystyle f'(x)=\frac{a'}{a}$
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$\frac{1}{\arctan\left(\mathrm{sinh}\left(x\right)\right)}\frac{d}{dx}\left(\arctan\left(\mathrm{sinh}\left(x\right)\right)\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of ln(arctan(sinh(x))). 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 arctangent. Multiplying fractions \frac{1}{\arctan\left(\mathrm{sinh}\left(x\right)\right)} \times \frac{1}{1+\mathrm{sinh}\left(x\right)^2}. Taking the derivative of hyperbolic sine.