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Applying the product rule for logarithms: $\log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right)$
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$\frac{d}{dx}\left(\sqrt[3]{\ln\left(x\right)+\ln\left(\mathrm{cosh}\left(x\right)\right)}\right)$
Learn how to solve problems step by step online. Find the derivative using logarithmic differentiation method d/dx(ln(xcosh(x))^1/3). Applying the product rule for logarithms: \log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right). The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. The derivative of a sum of two or more functions is the sum of the derivatives of each function. 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}.