Find First Derivative of 2/(e^x + e^-x)

[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 e^x is e^x...but should I move the denominator to the numerator first?

 

[jeffreydk]

You need to use the chain rule.

 

[Jason03]

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

 

[berkeman]

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.

 

[Ouabache]

Both forms of chain rule work fine.. (product or quotient).. here's a http://www.1728.com/chainrul.htm

 

[berkeman]

Cool website, Ouabache!

 

[Jason03]

for the following problem

$$<br /> \int {x(5x)^{-x^2}dx}<br />$$

wouldnt this simplify to

$$<br /> \int{5x^{-1}dx}<br />$$

 

[jeffreydk]

I don't think those two integrals are equivalent.

 

[Jason03]

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

$$<br /> \int {x}{(5^{-x^2})dx}<br />$$

 

[Dick]

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