finding the derivative of an exponential function

[coolbeans33]

So it's asking us to find y' and y'' when y=xe^-x

I know that the derivative of e^x is is just e^x, but this confuses me.

 

[stapel]

So it's asking us to find y' and y'' when y=xe^-x

I know that the derivative of e^x is is just e^x, but this confuses me.

What is the "this" which confuses you? You know the derivative of "x", you know the derivative of "e^x", and you know the product rule. Where are you getting stuck?

Please be complete. Thank you!

 

[coolbeans33]

What is the "this" which confuses you? You know the derivative of "x", you know the derivative of "e^x", and you know the product rule. Where are you getting stuck?

Please be complete. Thank you!

ok so I solved for the first derivative with the product rule:

e^-x+x(-e^-x)

there might be ways to simplify it more, but thats as far as I got. (Although I'm pretty sure the final answer is -e^-x(x-1). I just don't know how to get there)

Then if you apply the product rule again in solving for the second derivative:

y''=-e^-x(1) + d/dx (-e^-x) * (x-1)

can you even take the derivative of -e^-x​? why or why not?

 

[Deleted member 4993]

ok so I solved for the first derivative with the product rule:

e^-x+x(-e^-x) ... factor e^-x out to get e^-x * (1 - x)...........simple algebra.

there might be ways to simplify it more, but thats as far as I got. (Although I'm pretty sure the final answer is -e^-x(x-1). I just don't know how to get there)

Then if you apply the product rule again in solving for the second derivative:

y''=-e^-x(1) + d/dx (-e^-x) * (x-1)

can you even take the derivative of -e^-x​?

why or why not?.... The answer to this question lies in the answer to the question "What are the properties of differentiable functions?". If you do not know the answer - consult your textbook or do a google search and tell us what you found.If you know the answer tell us what you know.

.

 

[HallsofIvy]

Okay, you are a noob poster so here I go jumping on you with both feet (but I did take off my hobnailed boots!). Do NOT simply do a problem for a poster- indicate where, if anywhere, they went wrong- which is why staple asked him to show what he had tried- and gives suggestions. Also, not a lot of people will open an attachment- too much danger of a computer virus. It's not that much harder to type what you do- especially if you take the time to learn Latex.

 

[HWilliams44]

Okay, you are a noob poster so here I go jumping on you with both feet (but I did take off my hobnailed boots!). Do NOT simply do a problem for a poster- indicate where, if anywhere, they went wrong- which is why staple asked him to show what he had tried- and gives suggestions. Also, not a lot of people will open an attachment- too much danger of a computer virus. It's not that much harder to type what you do- especially if you take the time to learn Latex.

Sorry!!! I'll remove the attachment.