Find the 15th derivative of f(x) = x-a/e^x ?

[max4000]

Today my teacher gave up this problem and I still don't know how to tackle it, since i'm not that familiar with the new term e.. Any help would be great!

 

[stapel]

Today my teacher gave up this problem and I still don't know how to tackle it, since i'm not that familiar with the new term e.. Any help would be great!

They were supposed to have covered the natural exponential at the same time they covered the natural log, back in algebra. We cannot here replace the week or two of classroom lectures that were involved in teaching that chapter in the algebra book. Instead, try here (exponentials) and here (logs).

Has your calculus class covered derivatives of exponentials at all, or will you be needing lesson-links for that, too? Thank you!

 

[HallsofIvy]

Today my teacher gave up this problem and I still don't know how to tackle it, since i'm not that familiar with the new term e.. Any help would be great!

You can write $\displaystyle f(x)= x- a/e^x= x- ae^{-x}$.

Do you not know the derivative of $\displaystyle e^{-x}$?

$\displaystyle e^x$ is the easiest function to differentiate: $\displaystyle (e^x)'= e^x$.

Knowing that, what is the derivative of $\displaystyle e^{-x}$?

 

[max4000]

You can write $\displaystyle f(x)= x- a/e^x= x- ae^{-x}$.

Do you not know the derivative of $\displaystyle e^{-x}$?

$\displaystyle e^x$ is the easiest function to differentiate: $\displaystyle (e^x)'= e^x$.

Knowing that, what is the derivative of $\displaystyle e^{-x}$?

the derivative of e^-x stay the same.. but i can't figure what to do with the variable e. My teacher sure love exponential, but don't really talk about it...

 

[stapel]

i can't figure what to do with the variable e.

...which is why you might want to study up on the topic, since "e" is not actually a variable.

 

[max4000]

...which is why you might want to study up on the topic, since "e" is not actually a variable.

... Maybe.. But it seems that everything i find online is not what the teacher gave...

 

[lookagain]

Today my teacher gave up this problem and I still don't know how to tackle it, since i'm not that familiar with the new term e.. Any help would be great!

max4000, by the way you typed it, and under the context of the problem being a 15th derivative,

I suspect the function is actually $\displaystyle \ f(x) \ = \ \dfrac{x - a}{e^x}.$


If that's the case, then you missed grouping symbols:

f(x) = (x - a)/e^x

 

[stapel]

... Maybe.. But it seems that everything i find online is not what the teacher gave...

Well, we weren't in your classroom, so you'll need to expand on this a bit. For instance, what is an example of something you've found online about the natural exponential "e" which contradicts what your instructor has told you? And what is the contradiction?

It may be just a matter of semantics, or perhaps the teacher misspoke, but we can't help correct errors that we can't see. Thank you!