# How would I solve this derivative?

1. Oct 25, 2011

### CrossFit415

f(x) = xe2x, x ε ℝ And determine the domain.

So I did...

f'(x) = xe2x $\bullet$ d/dx 2

I applied the chain rule. I'm not sure if I did this right.

2. Oct 25, 2011

### iamalexalright

you'll have to use the product rule AND the chain rule

3. Oct 25, 2011

### CrossFit415

Ahh I see thank you

4. Oct 25, 2011

### Staff: Mentor

And in that order.

5. Oct 25, 2011

### CrossFit415

Okay cool!

6. Oct 25, 2011

### CrossFit415

So I applied the product rule 1st;

f(x) = xe2x
f'(x) = xe(2x) + xe(2)

Did I do this correctly?

7. Oct 25, 2011

### iamalexalright

Not correct:

First, what is the derivative of e^(2x) ?

Second, if f and g are arbitrary functions of x, what is the derivative of f*g with respect to x (ie, what does the product rule say)?

8. Oct 25, 2011

### CrossFit415

derivative of e2x is 2e?

9. Oct 25, 2011

### iamalexalright

Nope !

Here we have to use the chain rule but before we get there, what is the derivative of e^(x)?

10. Oct 25, 2011

### CrossFit415

Just ex

So...

e2x = 2ex ?

11. Oct 25, 2011

### iamalexalright

Close but you are missing one thing.

Maybe if you saw another example it would become more clear...
What is the derivative of sin(2x)?

Or if you prefer by the definition of the chain rule:
$(f \circ g)' = f'(g) * g'$

In your case, what is f and what is g?
Then can you see your mistake?