Final answer to the problem
$\frac{\mathrm{cosh}\left(x\right)}{\left(1+\mathrm{sinh}\left(x\right)^2\right)\arctan\left(\mathrm{sinh}\left(x\right)\right)}$
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Step-by-step Solution
Learn how to solve basic differentiation rules 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.
Final answer to the problem
$\frac{\mathrm{cosh}\left(x\right)}{\left(1+\mathrm{sinh}\left(x\right)^2\right)\arctan\left(\mathrm{sinh}\left(x\right)\right)}$
