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The logarithm of a quotient is equal to the logarithm of the numerator minus the logarithm of the denominator
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$\frac{d}{dx}\left(\ln\left(x\cot\left(x\right)\right)-\ln\left(\left(1+x^2\right)^3\right)\right)$
Learn how to solve problems step by step online. Find the derivative using logarithmic differentiation method d/dx(ln((xcot(x))/((1+x^2)^3))). The logarithm of a quotient is equal to the logarithm of the numerator minus the logarithm of the denominator. Using the power rule of logarithms: \log_a(x^n)=n\cdot\log_a(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.