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Applying the product rule for logarithms: $\log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right)$
Learn how to solve logarithmic differentiation problems step by step online.
$\frac{d}{dx}\left(\ln\left(\cos\left(x\right)\right)+\ln\left(x\right)\right)$
Learn how to solve logarithmic differentiation problems step by step online. Find the derivative using logarithmic differentiation method d/dx(ln(cos(x)x)). 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 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}. The derivative of the cosine of a function is equal to minus the sine of the function times the derivative of the function, in other words, if f(x) = \cos(x), then f'(x) = -\sin(x)\cdot D_x(x).