Find f^(')(x) where f(x)=3x cos(x).

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Identify components: Identify the components of the function that will require the use of the product rule. The function f(x) = 3x cos(x) is a product of two functions, g(x) = 3x and h(x) = cos(x).Recall product rule: Recall the product rule for differentiation. The product rule states that the derivative of a product of two functions is the derivative of the first function times the second function plus the first function times the derivative of the second function. In formula terms, if f(x) = g(x)h(x), then f'(x) = g'(x)h(x) + g(x)h'(x).Differentiate first function: Differentiate the first function g(x) = 3x. The derivative of g(x) with respect to x is g'(x) = d/dx(3x) = 3.Differentiate second function: Differentiate the second function h(x) = cos(x). The derivative of h(x) with respect to x is h'(x) = d/dx(cos(x)) = -sin(x).Apply product rule: Apply the product rule using the derivatives from steps 3 and 4. Using the product rule, f'(x) = g'(x)h(x) + g(x)h'(x) = 3 * cos(x) + 3x * (-sin(x)).Simplify derivative: Simplify the expression for the derivative. f'(x) = 3cos(x) - 3xsin(x).

Find $f'(x)$ where $f(x)=3x\cos(x)$ .

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Find f′(x)f'(x)f′(x) where f(x)=3xcos⁡(x)f(x)=3x\cos(x)f(x)=3xcos(x).

Find $f'(x)$ where $f(x)=3x\cos(x)$ .