calculate the derivative function of $f(z)=6ln(3z).$ $f(z)=$

Explanation:

Step1: Use chain - rule

The derivative of $\ln(u)$ is $\frac{u'}{u}$. Here $u = 3z$ and the function is $y=6\ln(3z)$. The derivative of a constant times a function is the constant times the derivative of the function.

Step2: Find $u'$

The derivative of $u = 3z$ with respect to $z$ is $u'=3$.

Step3: Calculate the derivative

$f'(z)=6\times\frac{3}{3z}$. Simplify the expression: $f'(z)=\frac{6}{z}$.

Answer:

$\frac{6}{z}$