The strength of a patient's reaction to a dose of x milligrams of a certain drug is  R(x) = 4x sqrt11+0.5x for 0 ≤ x ≤ 180. The derivative R'(x) is called the sensitivity to the drug. Find  R'(50), the sensitivity to a dose of 50 mg.

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A: given:

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A: Explanation of the answer is as follows

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A: on doing differentiation we get

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A: Derivative of the function is given below

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A: The derivative is calculated as:

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A:

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A: To determine the first derivative of the function.

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