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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 $g=2x-\sin\left(2x\right)$
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$\frac{d}{dx}\left(\cos\left(x\right)\right)\left(2x-\sin\left(2x\right)\right)+\cos\left(x\right)\frac{d}{dx}\left(2x-\sin\left(2x\right)\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of cos(x)(2x-sin(2x)). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=\cos\left(x\right) and g=2x-\sin\left(2x\right). The derivative of the cosine of a function is equal to minus the sine of the function times the derivative of the function, in other words, if f(x) = \cos(x), then f'(x) = -\sin(x)\cdot D_x(x). Simplify the product -(2x-\sin\left(2x\right)). The derivative of a sum of two or more functions is the sum of the derivatives of each function.