Find the derivative of $\ln\left(\frac{x\sqrt{x^2+3}}{\sqrt[3]{\left(x+9\right)^{2}}}\right)$

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$\frac{d}{dx}\left(\ln\left(x\right)+\frac{1}{2}\ln\left(x^2+3\right)-\frac{2}{3}\ln\left(x+9\right)\right)$

Learn how to solve problems step by step online. Find the derivative of ln((x(x^2+3)^1/2)/((x+9)^2/3)). 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 (\frac{1}{2}) is equal to the constant times the derivative of the function. The derivative of a function multiplied by a constant (-\frac{2}{3}) is equal to the constant times the derivative of the function.