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Suppose \( f^{\prime}(5)=3 \) and \( g^{\prime}(5)=6 \) Find \( h^{\prime}(5) \) where \( h(x)=2 f(x)+5 g(x)+5 \) \( h^{\prime}(5)=\square \)

Ask by Osborne Maxwell. in the United States
Mar 11,2025

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\( h^{\prime}(5)=36 \)

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To find \( h^{\prime}(5) \), we can differentiate \( h(x) \): \[ h(x) = 2 f(x) + 5 g(x) + 5 \] Using the derivative rules, we get: \[ h^{\prime}(x) = 2 f^{\prime}(x) + 5 g^{\prime}(x) \] Now, substituting \( x = 5 \): \[ h^{\prime}(5) = 2 f^{\prime}(5) + 5 g^{\prime}(5) \] Given \( f^{\prime}(5) = 3 \) and \( g^{\prime}(5) = 6 \), we can plug those values into our equation: \[ h^{\prime}(5) = 2(3) + 5(6) = 6 + 30 = 36 \] So, \( h^{\prime}(5) = \boxed{36} \).

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