Why does e^x - e^x=e^x?
and why does e^x + e^x = e^x?

This doesn't make sense. I know that the derivative of e^x=e^x, that makes sense. But the adding and subtracting 2 of them to = the same thing is weird.

There are several examples in my book that show this. Please explain?

I would highly advise looking in your book one more time, because what you've written simply isn't true,

y-y=0 for any and all y, including y=e^x

y+y=2y for any and all y, including y=e^x

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I could be wrong but could several other websites be wrong? I suppose they could...please see this about the problem:

Derivatives of exponential and logarithmic functions - An approach to calculus

"The derivative of ex with respect to x
is equal to ex."

I am fully aware that the derivative of
and that's what makes it special, but you wrote



and

which is nonsense

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derivative of e^x = e^x

and i looked whole pages you stated
and found nothing about

e^x - e^x = e^x
e^x + e^x = e^x

which doesn't make sense to me...?

since e^1 = 2.718281828
and in (e^x - e^x) here,
x = x
so
e^x - e^x = 0


e^x + e^x = 2e^x i guess

I agree, it is nonsense. Which is why I don't understand it.
For example, a problem has (2+3)e^-3x + (2+3)e^-3x = 10^e-3x.

Only one ^e-3x. So why when they add two of them does it only equal one?

2 + 3 = 5. So you have (5 + 5) = 10 lots of e^{-3x}.

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so are you saying that e^{-3x} is used as a suffix in this case, and even though the 5 and 5 are added together (thanks for helping with that sum LOL) the e^{-3x} is not added?

Let A represent e^{-3x}. It's very obvious that 5A + 5A = 10A.

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It may be obvious to super smart folks like you, I'm just a lowly biotechnologist and my current job in cancer research doesn't require calculus so I am resigned to being referred to as dumb. Condescend away!!! I don't mind at all.
Thank you for elucidating that you do not add the suffix together. Then why was everyone in the posts above telling me that if you add two of them together it does not equal one?

Not trying to be condescending here, but here's by best shot

one "e to the x" plus one "e to the x" equals 2 "e to the x"

You add the coefficients and keep the same

This is not any different from adding
to

You have 3 of "something" and you add 5 of "something" so you get 8 "somethings" i.e.

now read what you originally wrote

FALSE

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I am so glad that math geniuses like you all exist. It keeps the rest of us from going insane, I tell you, INSANE! Thank you tons, I completely understand now.
I give you the imaginary medal of "Smarty Pants & Extra Patient Math Helper and Super Explainer of Concepts".
(sorry, it's late and I've done about 12 hours of calculus today, seriously)

I learned that ac+ bc= (a+ b)c in the seventh grade. And that's all that is being used here: 3e^x+ 5e^x= (3+ 5)e^x= 8e^x. I will concede that I did not start calling that the "distributive law" until much later.