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