Final answer to the problem
$\frac{\mathrm{coth}\left(3x\right)}{x}-3\mathrm{csch}\left(3x\right)^2\ln\left(x\right)$
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Step-by-step Solution
Learn how to solve product rule of differentiation problems step by step online. Find the derivative of ln(x)coth(3x). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=\ln\left(x\right) and g=\mathrm{coth}\left(3x\right). 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}. Multiply the fraction by the term . Taking the derivative of hyperbolic cotangent.
Final answer to the problem
$\frac{\mathrm{coth}\left(3x\right)}{x}-3\mathrm{csch}\left(3x\right)^2\ln\left(x\right)$
