The derivative of y = e^x is y' = e^x. Why?

[henry200]

I need help with this question.....Why does the function y=e^x+c have a derivative that is itself for all values of c.

thanks in advance for your help.

 

[stapel]

Short answer: "Because". It just does.

Long answer: How far have you gotten in finding the derivative of f(x) = y, where y' = y, by separation of variables? What did you find?

Please be complete. Thank you!

Eliz.

 

[Deleted member 4993]

Re: derivative of y=e^x

I need help with this question.....Why does the function y=e^x+c have a derivative that is itself for all values of c.

thanks in advance for your help.

According to some mathematicians

the definition of e^x is that - the derivative of the function is the function itself. (or the growth rate is directly proportional to its size)

 

[skeeter]

\(\displaystyle \L y = e^x\)

take the natural log of both sides ...

\(\displaystyle \L \ln{y} = x\)

take the derivative of the equation w/r to x ...

\(\displaystyle \L \frac{d}{dx}[\ln{y} = x]\)

\(\displaystyle \L \frac{y'}{y} = 1\)

\(\displaystyle \L y' = y = e^x\)