# First derivative

1. Sep 7, 2008

### Jason03

Im trying to find the first derivative of the following equation:

$$\frac{2}{e^x+e^{-x}}$$

Im trying to figure how to approach this....

i know the derivative of ex is ex....but should I move the denominator to the numerator first?

Last edited: Sep 7, 2008
2. Sep 7, 2008

### jeffreydk

You need to use the chain rule.

3. Sep 7, 2008

### Jason03

not to be a pest...but im a little rusty on the chain rule....how would that apply?

4. Sep 7, 2008

### Staff: Mentor

There are formulas for the derivitave of a product and of a quotient. Are you familiar with them? If you're not familiar with the derivative of a quotient, you can express the quotient as a product:

$$\frac{A}{B} = A * B^{-1}$$

And use your usual equation for the derivative of a product.

5. Sep 7, 2008

### Ouabache

Both forms of chain rule work fine.. (product or quotient).. here's a refresher

Last edited: Sep 7, 2008
6. Sep 7, 2008

### Staff: Mentor

Cool website, Ouabache!

7. Sep 8, 2008

### Jason03

for the following problem

$$\int {x(5x)^{-x^2}dx}$$

wouldnt this simplify to

$$\int{5x^{-1}dx}$$

8. Sep 8, 2008

### jeffreydk

I don't think those two integrals are equivalent.

9. Sep 8, 2008

### Jason03

actually I wrote the first expression wrong ....this is what the first expression should be...

$$\int {x}{(5^{-x^2})dx}$$

10. Sep 8, 2008

### Dick

Change the 5^(-x^2) to a power of e instead. Then use a u substitution.