Question

Derivative of x^r * e^sx

Answer 1

\[\Large\bf\sf x^r\cdot e^{sx}\]We need to take the derivative of this with respect to x?

Answer 2

yes. The r throws me off

Answer 3

TEAM JACOBBBBBB!!!!

Answer 4

I'm jkjk jk lol.. ive never actually seen the movies.. just read your profile XD trying to stir up trouble.

Answer 5

ok ok anyway, the problem here.. let's see

Answer 6

\[\Large\bf\sf \left(x^r\cdot e^{sx}\right)'\quad=\quad \color{royalblue}{\left(x^r\right)'}e^{sx}+x^r\color{royalblue}{\left(e^{sx}\right)'}\]We have the product of two functions of x.
So here is our product rule setup.

We need to take the derivative of the blue parts.
The first one is giving you trouble?

Answer 7

yes, the first part

Answer 8

Would it be 0 because of r or no?

Answer 9

Just power rule silly! :O

Answer 10

\[\Large\bf\sf (x^5)'\quad=\quad 5x^{5-1}\]

Answer 11

\[\Large\bf\sf (x^r)'\quad=\quad ?\]

Answer 12

rx^r-1?

Answer 13

good good good.

Answer 14

\[\Large\bf\sf \left(x^r\cdot e^{sx}\right)'\quad=\quad \color{orangered}{\left(rx^{r-1}\right)}e^{sx}+x^r\color{royalblue}{\left(e^{sx}\right)'}\]

Answer 15

Understand how to do the other blue part?

Answer 16

ohh! okay! the other is se^sx

Answer 17

That almost looks like a bad word!! :O
But yes good job! :)

Answer 18

haha! Thank You so much!