Question

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

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:

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