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Step-by-step Solution
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Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=\cos\left(x\right)$ and $g=-\ln\left(x\right)$
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$-\frac{d}{dx}\left(\cos\left(x\right)\right)\ln\left(x\right)+\cos\left(x\right)\frac{d}{dx}\left(-\ln\left(x\right)\right)$
Learn how to solve problems step by step online. Find the derivative using the product rule d/dx(-cos(x)ln(x)). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=\cos\left(x\right) and g=-\ln\left(x\right). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=\ln\left(x\right) and g=-1. The derivative of the constant function (-1) is equal to zero. Any expression multiplied by 0 is equal to 0.