derivative of the function y=e^x

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Calc12

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Nov 17, 2010
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f(x)= (e^x +1)^2

I am not sure how to find the derivative of this one!

Do I (e^x +1)(e^x +1)?

Thanks in advance!
 


You could multiply it all out, and then derivate the resulting product, but I suspect that this exercise is intended to demonstrate your knowledge of the Chain Rule.

In other words, if you apply the Chain Rule, there is no need to first expand the square.

f(x) = (e^x + 1)^2 is a composite function (i.e., a function "inside" another function).

The outer function is the squaring function:

f(x) = (stuff)^2

The inner function is the exponential expression e^x + 1.

The Chain Rule tells us that when we determine the derivative of a composite function, it's the derivative of the outer function multiplied by the derivative of the inner function.

What is the derivative of (stuff)^2 ?

Note that this derivative does not depend on the actual expression inside the parentheses. You deal with "stuff" in the next step. Just use the Power Rule, here.

What is the derivative of e^x + 1 ?

Multiply these two derivatives together, and you've got it. What say you now?

 


Looks good!

Here's a minor (ticky-tacky) point:

dy/dx is okay notation, as long as the symbols y and f(x) mean the same thing. Do your materials state that y = f(x)?

Otherwise, I'd represent the derivative of the given function f as f`(x).

I mention this point because your original post defines f(x) as one thing and y as something else (look at your subject line).

Cheers!

 


I view the expanded expression as neither a simplification nor an unsimplification. I mean, either version is a correct answer, from my point-of-view, but some instructors and machine teachers might disagree. Even so, in the absence of explicit instructions to report a specific form, you're good to go (in my book).

 
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