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Simplify the derivative by applying the properties of logarithms
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$\frac{d}{dx}\left(\frac{\ln\left(x\right)+\ln\left(\cos\left(x\right)\right)}{\frac{1}{2}\ln\left(x+1\right)}\right)$
Learn how to solve problems step by step online. Find the derivative d/dx(ln(xcos(x))/ln((x+1)^1/2)). Simplify the derivative by applying the properties of logarithms. Apply the quotient rule for differentiation, which states that if f(x) and g(x) are functions and h(x) is the function defined by {\displaystyle h(x) = \frac{f(x)}{g(x)}}, where {g(x) \neq 0}, then {\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}. The power of a product is equal to the product of it's factors raised to the same power. Simplify the product -(\ln\left(x\right)+\ln\left(\cos\left(x\right)\right)).