Question

Compute the derivative of the following functions. $$f(x)=15 e^{3 x}$$

   Compute the derivative of the following functions.
$$f(x)=15 e^{3 x}$$

Calculus for Scientists and Engineers: Early Transcendental

William Briggs, Lyle… 1st Edition

Chapter 3, Problem 45

Instant Answer

Solved by Expert Amy Jiang

05/27/2020

Step 1

Step 1: First, we identify the function that we are asked to differentiate, which is $f(x)=15 e^{3 x}$. Show more…

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Compute the derivative of the following functions. $$f(x)=15 e^{3 x}$$

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Key Concepts

Exponential Function Differentiation

This concept involves understanding the derivative of exponential functions. When differentiating an exponential function like e^(kx), the result is k * e^(kx) due to the inherent properties of the exponential function and its rate of change.

Chain Rule

The chain rule is applied when differentiating composite functions. It states that if you have a function composed of another function, for instance e^(g(x)), the derivative is obtained by differentiating the outer function with respect to the inner function and then multiplying by the derivative of the inner function g(x), which results in k * e^(kx) when g(x) = kx.

Constant Multiple Rule

The constant multiple rule indicates that when a function is multiplied by a constant, the derivative of the product is the constant multiplied by the derivative of the function. This rule simplifies the differentiation process for functions that include a scalar factor.

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