Simple Derivative: e^nx Answer C

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In summary, the conversation is about finding the derivative of e^nx, and the correct answer is not (C) but rather considering the higher order derivatives as well.
  • #1
Qube
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Homework Statement

http://k.minus.com/j4eToABCaFgrW.png

Homework Equations



The derivative of e^anything = e^anything * (du/dx).

The Attempt at a Solution



So, wouldn't the answer choice be C? The derivative of e^nx = (e^nx)(n).
 
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  • #2
Qube said:

Homework Statement

http://k.minus.com/j4eToABCaFgrW.png

Homework Equations



The derivative of e^anything = e^anything * (du/dx).

The Attempt at a Solution



So, wouldn't the answer choice be C? The derivative of e^nx = (e^nx)(n).
No, it's not answer (C). (C) is the first derivative !

Start by looking at [itex]\displaystyle \frac{d}{dx}e^{nx}\,,\ \ \frac{d^2}{dx^2}e^{nx}\,,\ \ \frac{d^3}{dx^3}e^{nx}\,, \ \ \text{etc.}[/itex]
 
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  • #3
Ohhh ... I get it :)! Thanks :D.
 

FAQ: Simple Derivative: e^nx Answer C

What is a "simple derivative"?

A simple derivative is the rate of change of a mathematical function at a specific point. It is calculated by finding the slope of the tangent line to the curve at that point.

What does "e^nx" mean in this context?

In this context, "e" represents the mathematical constant approximately equal to 2.718, and "n" is a constant number. The variable "x" represents the input value of the function.

3. How do you find the derivative of e^nx?

To find the derivative of e^nx, you can use the power rule of differentiation, which states that the derivative of a function raised to a constant power is equal to the constant multiplied by the function raised to the power minus one. In this case, the derivative of e^nx is equal to n*e^nx.

4. What is the purpose of finding the derivative of e^nx?

Finding the derivative of e^nx allows us to understand the rate of change of the function at a specific point. This information is useful in many fields of science, such as physics and economics, where understanding the rate of change of a quantity is important.

5. Can the derivative of e^nx be used to solve real-world problems?

Yes, the derivative of e^nx can be used to solve real-world problems. For example, it can be used to model the growth or decay of a population over time, or to calculate the velocity of an object at a specific point in time. It is a fundamental concept in calculus and has many practical applications in various scientific fields.

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