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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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$\frac{d}{dx}\left(\ln\left(x\right)+\ln\left(\left(x^2-2\right)^3\right)\right)$
Learn how to solve problems step by step online. Find the derivative using logarithmic differentiation method d/dx(ln(x(x^2-2)^3)). Applying the product rule for logarithms: \log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right). Using the power rule of logarithms: \log_a(x^n)=n\cdot\log_a(x). The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function.