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

Question

zepdrix · Answer

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? :)

imtant · Answer

Use product rule.

zepdrix · Answer

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

zepdrix · Answer

y'=, sorry typo

imtant · Answer

It's okay.

zepdrix · Answer

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

imtant · Answer

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

imtant · Answer

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

zepdrix · Answer

Ya looks good.
We could factor out an e^x if we want.

$$\Large y'=e^x(1+x)$$

zepdrix · Answer

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

imtant · Answer

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

zepdrix · Answer

yay good job \c:/

zepdrix · Answer

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

imtant · Answer

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