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Simplify the derivative by applying the properties of logarithms
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$\frac{d}{dx}\left(3\ln\left(x-9\right)+\ln\left(6x^3\right)-\frac{1}{5}\ln\left(x-2\right)\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of ln(((x-9)^36x^3)/((x-2)^1/5)). Simplify the derivative by applying the properties of logarithms. 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}.