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Simplify the derivative by applying the properties of logarithms
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$\frac{d}{dx}\left(\frac{x\ln\left(x^2+2x+1\right)}{\cos\left(1-x\right)}\right)$
Learn how to solve problems step by step online. Find the derivative of x/cos(1-x)ln(x^2+2x+1). 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}}. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=x and g=\ln\left(x^2+2x+1\right). The derivative of the linear function is equal to 1.