suppose that $f(x)=19e^{x}+13ln(x)$. find $f(3)$. f(3) = submit answer next item attempt 1: 2 attempts…

Explanation:

Step1: Find the derivative of (f(x))

The derivative of (y = 19e^{x}) is (y^\prime=19e^{x}) (since the derivative of (e^{x}) is (e^{x})), and the derivative of (y = 13\ln(x)) is (y^\prime=\frac{13}{x}) (using the formula ((\ln x)^\prime=\frac{1}{x})). So (f^\prime(x)=19e^{x}+\frac{13}{x}).

Step2: Evaluate (f^\prime(x)) at (x = 3)

Substitute (x = 3) into (f^\prime(x)): (f^\prime(3)=19e^{3}+\frac{13}{3}).

Answer:

(19e^{3}+\frac{13}{3})