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10 votes
10 votes

(4 * 3^x)'

Evaluate

User Cleary
by
3.2k points

1 Answer

19 votes
19 votes

Answer:


\approx 4.39 \cdot 3^x

Explanation:

Recall a property:


(c\cdot f(x))'=c\cdot f(x)', where
c is a constant.

Apply the property to the task:


(4\cdot 3^(x))'=4\cdot (3^x)'

Recall a property of the derivative of an exponential function:


(a^x)'=a^x \cdot ln(a)

Apply the property to the task:


4\cdot 3^x \cdot \ln 3

Since
\ln 3\approx 1.0986, it follows:


4\cdot 3^x \cdot \ln 3 \approx 4\cdot 1.0986 \cdot \ln3

Multiply the numbers.

The answer is about
4.39\cdot 3^x.

User Dynalon
by
2.2k points