Derivative of exponential function

The summary of the conversation is that Sheldon is seeking clarification on whether his answer (e^x / (1 + e^x)^2) is correct, as Kline's Calculus book gives a different answer (1 / (1 + e^x)). The other person in the conversation confirms that Sheldon's answer is correct and suggests using the website calc101.com for checking derivatives. Sheldon thanks them both for their help. In summary, Sheldon is seeking clarification on the correct answer for the derivative of y = e^x / (1 + e^x) and is given confirmation and a resource for checking derivatives
  • #1
SheldonG
50
0

Homework Statement


find y', [tex] y = \frac{e^x}{1+e^x}[/tex]

Homework Equations


derivative of e^x = e^x, quotient rule.

The Attempt at a Solution



The old man is back, sorry, and I don't seem to be able to enter this using the tex stuff.
This is from Kline's Calculus, page 348. I proceed as follows:

y' = [(1+e^x)(e^x)-e^x(e^x)]/(1+e^x)^2 --- the quotient rule.

Simplifying:

y' = e^x/(1+e^x)^2

However, Kline gives 1/(1+e^x).

I am at a loss. Thanks for any suggestions.

Sheldon
 
Last edited:
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  • #2
I believe your answer is correct
 
  • #3
You can check on www.calc101.com, it shows how derivatives are done. Your answer is correct, Klines books weren't very well edited >.<
 
  • #4
Thank you both very much. Also for the calc101 link.

Sheldon
 

FAQ: Derivative of exponential function

What is the derivative of an exponential function?

The derivative of an exponential function can be found by taking the original function and multiplying it by the natural logarithm of the base. In other words, if the original function is f(x) = a^x, then the derivative is f'(x) = ln(a) * a^x.

Why is the derivative of an exponential function important?

The derivative of an exponential function is important because it helps us understand the rate of change of the function at any given point. This can be useful in various applications, such as modeling population growth or predicting stock market trends.

What is the difference between the derivative of an exponential function and a logarithmic function?

The derivative of an exponential function involves the natural logarithm of the base, while the derivative of a logarithmic function involves the reciprocal of the argument. In simpler terms, the exponential function's derivative involves multiplication while the logarithmic function's derivative involves division.

How do you find the derivative of a composite exponential function?

To find the derivative of a composite exponential function, you can use the chain rule. First, take the derivative of the outer function, and then multiply it by the derivative of the inner function. For example, if the function is f(x) = e^(x^2), the derivative would be f'(x) = 2x * e^(x^2).

What is the relationship between the derivative of an exponential function and its original function?

The derivative of an exponential function is directly proportional to the original function. In other words, as the original function increases or decreases, the derivative also increases or decreases proportionally. This can be seen in the equation f'(x) = ln(a) * a^x, where the derivative is always a multiple of the original function.

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