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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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$\frac{d}{dx}\left(\ln\left(5\right)+\ln\left(x\right)\right)$
Learn how to solve problems step by step online. Find the derivative using logarithmic differentiation method d/dx(ln(5x)). Applying the product rule for logarithms: \log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right). The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of the constant function (\ln\left(5\right)) is equal to zero. 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}.