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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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$\frac{d}{dx}\left(\frac{\ln\left(4\right)+\ln\left(x\right)}{\ln\left(2x\right)}\right)$
Learn how to solve sum rule of differentiation problems step by step online. Find the derivative using logarithmic differentiation method d/dx(ln(4x)/ln(2x)). 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 quotient rule for differentiation, which states that if f(x) and g(x) are functions and h(x) is the function defined by {\displaystyle h(x) = \frac{f(x)}{g(x)}}, where {g(x) \neq 0}, then {\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}. Simplify the product -(\ln\left(4\right)+\ln\left(x\right)).