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$\frac{d}{dx}\left(\cos\left(2x\right)^{3}\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of cos(2x)^2cos(2x). Simplifying. 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). The derivative of the linear function times a constant, is equal to the constant.