Question

Ho to differentiate y=xe^x into first and second derivative?

Answer 1

Hmm, we have the product of 2 functions of x.\[\Large f=x,\qquad g=e^x\]
What do we do when we have a product? :)

Answer 2

Use product rule.

Answer 3

Yessss good good good!\[\Large y=f'g+fg'\]

Answer 4

y'=, sorry typo

Answer 5

It's okay.

Answer 6

Remember the derivative of e^x?
Understand how to find the first derivative or still confused? :o

Answer 7

The first derivative I got e^x+xe^x.Is it right?

Answer 8

Yes I remember.It will still be e^x.right?

Answer 9

Ya looks good.
We could factor out an e^x if we want.

\[\Large y'=e^x(1+x)\]

Answer 10

Looks like we'll have a similar setup for the second derivative.\[\Large f=(1+x), \qquad g=e^x\]

Answer 11

So,I will get for second derivative is 2e^x+xe^x?

Answer 12

yay good job \c:/

Answer 13

Again you could factor,\[\Large y''=e^x(2+x)\]
And you might see the pattern that is emerging! :)

Answer 14

Ok,zepdrix.Thanks. :) I got it.