Find the derivative of $x^x\ln\left(9x\arccos\left(x\right)\right)$

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$\frac{d}{dx}\left(x^x\left(\ln\left(x\right)+\ln\left(9\arccos\left(x\right)\right)\right)\right)$

Learn how to solve differential calculus problems step by step online. Find the derivative of x^xln(9xarccos(x)). Simplify the derivative by applying the properties of logarithms. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x^x and g=\ln\left(x\right)+\ln\left(9\arccos\left(x\right)\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}.