Differentiate using chain rule

1. Oct 25, 2007

v_pino

Hi everyone,

I'm new to this forum... I hope I've posted in the right section...

How do I differentiate y=2e(2x+1) using the chain rule?

I let u= (2x+1)

so du/dx = 2

but how do I differentiate y= 2eU ?

thank you :)

2. Oct 25, 2007

Hurkyl

Staff Emeritus
Well, I see a multiplication and an exponentiation in that expression...

3. Oct 25, 2007

v_pino

Does it mean that I should use the chain rule again?

and I get dy/du = 2eU

so dy/dx = 4e(2x+1) ?

Last edited: Oct 25, 2007
4. Oct 25, 2007

HallsofIvy

Staff Emeritus
The fact that a problem uses the word "differentiate" does not mean it is a differential equation! I am moving this to the Calculus and Analysis forum.

5. Oct 25, 2007

HallsofIvy

Staff Emeritus
First, do you mean
[tex]y= 2e^{2x+1}[/itex]
which in "ASCII" would be y= 2e^(2x+1). What you wrote, I would interpret as 2e times(2x+1) and there is no need for the chain rule!

If you let u= 2x+1, then, yes, the chain rule says that the derivative of y= 2e^u, with respect to x, is dy/dx= 2e^u (du/dx). Since you have already determined that du/dx= 2, that is dy/dx= 2e^(2x+1) (2)= 4 e^(2x+1). There is no need for a second application of the chain rule.

6. Oct 25, 2007

v_pino

thank you very much :)