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Simplify the derivative by applying the properties of logarithms
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$\frac{d}{dx}\left(\ln\left(x\left(x+1\right)\right)\right)$
Learn how to solve integral calculus problems step by step online. Find the derivative using logarithmic differentiation method d/dx(ln(x(x^2^1/2+1))). Simplify the derivative by applying the properties of logarithms. 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. 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}.