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The derivative of a function multiplied by a constant ($2$) is equal to the constant times the derivative of the function
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$2\frac{d}{dx}\left(\cos\left(x\right)^2\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of 2cos(x)^2. The derivative of a function multiplied by a constant (2) is equal to the constant times the derivative of the function. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. 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). Expand and simplify.