19. find the derivative of $f(x)=x^{ln(3)}$. $f(x)=$

Explanation:

Step1: Recall power - rule for differentiation

The power - rule states that if $y = x^n$, where $n$ is a constant, then $y^\prime=nx^{n - 1}$. Here, $n=\ln(3)$ (since $\ln(3)$ is a constant).

Step2: Apply the power - rule

For the function $f(x)=x^{\ln(3)}$, by the power - rule $f^\prime(x)=\ln(3)x^{\ln(3)-1}$.

Answer:

$\ln(3)x^{\ln(3)-1}$