Math Help - Urgent differential help!!

1. Urgent differential help!!

Hey guys

can you help with this please?

9) Differentiate $xe^{\sqrt{x}}$

thankyou guys!

2. Originally Posted by anthmoo
Hey guys

can you help with this please?

9) Differentiate $xe^{\sqrt{x}}$

thankyou guys!
we need the product rule here:

recall, by the product rule: $\frac d{dx}f(x)g(x) = f'(x)g(x) + f(x)g'(x)$

also recall that $\frac d{dx}e^u = u'e^u$, where $u$ is a function of $x$

try it and see what you get

3. I did...but I keep getting 5e^2

I think its differentiating $e^{\sqrt{x}}$ that's the problem. Can you help with that?

4. Originally Posted by anthmoo
I did...but I keep getting 5e^2

I think its differentiating $e^{\sqrt{x}}$ that's the problem. Can you help with that?
did you see my last post? when finding the derivative of e to some power, you find the derivative of the power and multiply it by e to the old power

example: $\frac d{dx}e^{x^2} = \frac d{dx}x^2 \cdot e^{x^2} = 2xe^{x^2}$

now try $\frac d{dx}e^{\sqrt{x}}$

5. Thankyou so much!

I can do it now =] all that was needed was that rule you gave for differentiating e to the power of a function. Thank you!

Anthmoo

6. Originally Posted by anthmoo
Thankyou so much!

I can do it now =] all that was needed was that rule you gave for differentiating e to the power of a function. Thank you!

Anthmoo

7. I got $2e^2$ ...that's right isn't it?

Thanks =]

8. Originally Posted by anthmoo
I got $2e^2$ ...that's right isn't it?

Thanks =]
No!! The only way you can get a constant after taking a derivative is if the original function is a constant times x. Does $e^{\sqrt{x}}$ look like $cx$?

Recall what Jhevon said:

Originally Posted by Jhevon
also recall that $\frac d{dx}e^u = u'e^u$, where $u$ is a function of $x$
Here we have $u = \sqrt{x}$. So what is $u^{\prime}$?

-Dan

9. Originally Posted by topsquark
No!! The only way you can get a constant after taking a derivative is if the original function is a constant times x. Does $e^{\sqrt{x}}$ look like $cx$?

Recall what Jhevon said:

Here we have $u = \sqrt{x}$. So what is $u^{\prime}$?

-Dan

Wait wait!! I'm sorry, the original question asked "if f'(4)"...if it was f'(4)...would that be right??

Thanks

10. Originally Posted by anthmoo
Wait wait!! I'm sorry, the original question asked "if f'(4)"...if it was f'(4)...would that be right??

Thanks
You tell me.
$u^{\prime} = \frac{1}{2\sqrt{x}}$

-Dan