Find (d)/(dx)(4cos 2x) Answer:

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Find  (d)/(dx)(4cos 2x) Answer:

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Identify Functions: We are given the function f(x) = 4cos(2x) and we need to find its derivative with respect to x. We will use the chain rule, which states that the derivative of a composite function is the derivative of the outer function evaluated at the inner function times the derivative of the inner function.Derivative of Outer Function: First, let's identify the outer function and the inner function. The outer function is cos(u) where u = 2x, and the inner function is 2x. We will need to take the derivative of the outer function with respect to u and then multiply it by the derivative of the inner function with respect to x.Derivative of Inner Function: The derivative of the outer function cos(u) with respect to u is -sin(u). So, the derivative of cos(2x) with respect to 2x is -sin(2x).Apply Chain Rule: The derivative of the inner function 2x with respect to x is 2. This is because the derivative of x with respect to x is 1, and the constant multiple rule states that the derivative of a constant times a function is the constant times the derivative of the function.Simplify Expression: Now, we apply the chain rule by multiplying the derivative of the outer function by the derivative of the inner function. This gives us the derivative of 4cos(2x) with respect to x as 4 * (-sin(2x)) * 2.Final Answer: Simplify the expression by multiplying the constants and keeping the function part as is. This results in -8sin(2x).We have found the derivative of 4cos(2x) with respect to x, which is -8sin(2x). This is our final answer.

Find $\frac{d}{d x}(4 \cos 2 x)$ $\newline$ Answer:

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Find $\frac{d}{d x}(4 \cos 2 x)$ $\newline$ Answer: