Differentiate the function.
\[
\begin{array}{l}
F(s)=\ln (\ln (9 s)) \\
F^{\prime}(s)=
\end{array}
\]

Answer

Expert–verified

Hide Steps

Answer

\(\boxed{F'(s) = \frac{1}{s \ln(9s)}}\) is the final answer.

Steps

Step 1 ：The problem is asking for the derivative of the function \(F(s) = \ln(\ln(9s))\).

Step 2 ：To solve this, we can use the chain rule of differentiation. The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function.

Step 3 ：In this case, the outer function is \(\ln(x)\) and the inner function is \(\ln(9s)\).

Step 4 ：Applying the chain rule, we get \(F'(s) = \frac{1}{s \ln(9s)}\).

Step 5 ：\(\boxed{F'(s) = \frac{1}{s \ln(9s)}}\) is the final answer.

Differentiate the function.\[\begin{array}{l}F(s)=\ln (\ln (9 s)) \\F^{\prime}(s)=\end{array}\]

Answer

Popular Problems

Differentiate the function.
\[
\begin{array}{l}
F(s)=\ln (\ln (9 s)) \\
F^{\prime}(s)=
\end{array}
\]