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** Step-by-step Solution **

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Simplify the derivative by applying the properties of logarithms

Learn how to solve limits of exponential functions problems step by step online.

$\frac{d}{dx}\left(\cos\left(3x-1\right)^{12}\right)$

Learn how to solve limits of exponential functions problems step by step online. Find the derivative of cos(3x-1)^4^3. Simplify the derivative by applying the properties of logarithms. 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 a sum of two or more functions is the sum of the derivatives of each function.

** Final answer to the problem

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