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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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$\frac{d}{dx}\left(\ln\left(\sqrt[5]{x}\right)+\ln\left(\left(x^2-4\right)^7e^x\right)\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative using logarithmic differentiation method ln(x^1/5(x^2-4)^7e^x). Applying the product rule for logarithms: \log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right). Applying the product rule for logarithms: \log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right). Apply the formula: \ln\left(e^x\right)=x. Using the power rule of logarithms: \log_a(x^n)=n\cdot\log_a(x).