Homework Help: Differentiate e^x and Trig Functions

1. May 3, 2010

gabyoh23

1. The problem statement, all variables and given/known data
Differentiate
e^x * cotx / 5sqrtx^2
[Sorry for not using the formatting things. They didn't seem to be working for me, and this is urgent!]

2. Relevant equations
The quotient rule seems like that's the way to go...

3. The attempt at a solution
At first I tried using the product rule on the numerator, then plugging that into the quotient rule formula, but that was needlessly complicated. So, I went straight into using the quotient rule, but I got a huge messy equation. Could anyone clarify what I SHOULD be getting?

All help is greatly appreciated!
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. May 3, 2010

jtyler05si

Both ways are correct. Either do product rule inside of Quotient or do Product then do Quotient. Both will be potentially messy.

3. May 3, 2010

jtyler05si

also is that 5sqrt(x^2) or (5sqrt(x))^2 or what?
because that should simple things out for you.

4. May 3, 2010

gabyoh23

It's 5sqrt(x^2).

5. May 3, 2010

gauss^2

The quotient rule is never worth remembering IMO. Just use the product rule and think of the derivative of a quotient as

$$\frac{d}{dx}\left( \frac{f(x)}{g(x)} \right) = \frac{d}{dx}\left(f(x) \ g(x)^{-1}\right)$$

and dont forget to apply the chain rule when differentiating $$g(x)^{-1}$$.

It's too easy to forget the quotient rule on an exam, and also too easy to screw it up when you're in a rush to get everything done in 50 minutes on a midterm. The product rule and chain rule are easy though, and critical to know anyways.

6. May 3, 2010

jtyler05si

What's the square root of x^2?

that will make it a little simpler.

Last edited: May 3, 2010