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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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$\frac{d}{dx}\left(\ln\left(x-1\right)-\ln\left(x\right)\right)$
Learn how to solve problems step by step online. Find the derivative using logarithmic differentiation method d/dx(ln((x-1)/x)). The logarithm of a quotient is equal to the logarithm of the numerator minus the logarithm of the denominator. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of a function multiplied by a constant is equal to the constant times the derivative of the 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}.