Find the derivative of the following function.
\[
g(t)=18 \sqrt{t}
\]

Answer

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Answer

Therefore, the derivative of the function is \(\boxed{\frac{9}{\sqrt{t}}}\).

Steps

Step 1 ：The derivative of a function can be found using the power rule, which states that the derivative of \(x^n\) is \(n \cdot x^{n-1}\).

Step 2 ：In this case, we can rewrite \(g(t)=18 \sqrt{t}\) as \(g(t)=18t^{0.5}\).

Step 3 ：Applying the power rule, we get \(g'(t)=0.5 \cdot 18t^{0.5-1}\).

Step 4 ：Simplifying this, we get \(g'(t)=9t^{-0.5}\).

Step 5 ：Therefore, the derivative of the function is \(\boxed{\frac{9}{\sqrt{t}}}\).