Differentiate e^x and Trig Functions

[gabyoh23]

Homework Statement

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!]

Homework Equations

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

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!

 

[jtyler05si]

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

 

[jtyler05si]

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

 

[gabyoh23]

It's 5sqrt(x^2).
Sorry about that.

 

[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 don't 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.

 

[jtyler05si]

What's the square root of x^2?

that will make it a little simpler.