Derivative of e^x with Exponential Functions - Homework Question and Solution

In summary, the derivative of e^x is simply e^x itself, found using the power rule. This is significant because it represents the rate of change of the function at any given point and has practical applications. For example, in population growth models, the derivative can determine the rate of growth at a specific time. The derivative and integral of e^x are not the same, as the integral includes a constant while the derivative is just e^x. They are inverse operations but not equivalent.
  • #1
n.a.s.h
18
0

Homework Statement


what is the derivative of e^[(-X^2-2x+1)/2]


Homework Equations





The Attempt at a Solution



Is this right?

= -(x+1)e^[(-x²-2x+1)]
 
Physics news on Phys.org
  • #2
n.a.s.h said:

Homework Statement


what is the derivative of e^[(-X^2-2x+1)/2]


Homework Equations





The Attempt at a Solution



Is this right?

= -(x+1)e^[(-x²-2x+1)]

No. It's -(x+1)e^[(-x²-2x+1)/2]. I'm going to guess that's what you meant to write.
 
  • #3
Use this:

[d/dx] e^f(x) = e^f(x) [d/dx] f(x)
 

FAQ: Derivative of e^x with Exponential Functions - Homework Question and Solution

What is the derivative of e^x?

The derivative of e^x is simply e^x itself. This is because the derivative of any exponential function is equal to the function itself.

How do you find the derivative of e^x?

To find the derivative of e^x, you can use the power rule. This means that you bring down the exponent and subtract 1 from it. So for e^x, the derivative would be e^x.

What is the significance of the derivative of e^x?

The derivative of e^x is important because it is the rate of change of the function e^x at any given point. It also has many real-world applications, such as in finance and growth models.

Can you give an example of using the derivative of e^x?

One example of using the derivative of e^x is in population growth models. If we have a population that is growing exponentially at a rate of e^x, the derivative of this function would give us the rate of growth at any given time.

Is the derivative of e^x the same as the integral of e^x?

No, the derivative and integral of e^x are not the same. The integral of e^x is e^x + C, where C is a constant, while the derivative is simply e^x. They are inverse operations of each other, but not equivalent.

Back
Top