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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 $f'(x) = -\sin(x)\cdot D_x(x)$
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$-\sin\left(2x-\sin\left(2x\right)\right)\frac{d}{dx}\left(2x-\sin\left(2x\right)\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of cos(2x-sin(2x)). 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). The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of the linear function times a constant, is equal to the constant. The derivative of a function multiplied by a constant (-1) is equal to the constant times the derivative of the function.