Check the solution to "Derivatives with exponentials Compute the derivative of the..."

Yasmin

Answered question

2021-10-03

Derivatives with exponentials Compute the derivative of the following functions.

f (x) = 15 e^{3 x}

tafzijdeq

Skilled2021-10-04Added 92 answers

Step 1
Use the two rules given as follows:
The derivative of a composite function is f[g(x)] is f'[g(x)]·g'(x).
The derivative of

e^{x} i s e^{x}

.
Step 2
Use the rules to differentiate the function f(x).

f^{'} (x) = \frac{d}{d (e^{3 x})} (15 e^{3 x}) \cdot \frac{d}{d x} (3 x)

= 15 e^{3 x} (3)

= 45 e^{3 x}

Step 3
Conclusion:

f^{'} (x) = 45 e^{3 x}

Jeffrey Jordon

Expert2022-08-14Added 2605 answers

Answer is given below (on video)

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