Simplifying a denominator before taking derivative

**beebe** · October 5th 2011, 06:13 PM

This might be more of a trig question, so if it is would someone kindly move it for me?

So I'm finding the second derivative of $ln[sec(x)+tan(x)]$ . My first derivative is $\frac{sec(x)tan(x)+sec^2(x)}{sec(x)+tan(x)}$ .

My question is: can I simplify this fraction to make taking the second derivative less tedious? I'm capable of doing it without simplifying first, but I don't want to get a super long and ugly answer.

**TKHunny** · October 5th 2011, 06:44 PM

Have you considered factoring out sec(x) from the numerator?

**Prove It** · October 5th 2011, 06:46 PM

Originally Posted by beebe

This might be more of a trig question, so if it is would someone kindly move it for me?

So I'm finding the second derivative of $ln[sec(x)+tan(x)]$ . My first derivative is $\frac{sec(x)tan(x)+sec^2(x)}{sec(x)+tan(x)}$ .

My question is: can I simplify this fraction to make taking the second derivative less tedious? I'm capable of doing it without simplifying first, but I don't want to get a super long and ugly answer.

Or you could multiply top and bottom by $\displaystyle \sec{x} - \tan{x}$ , since you should know that $\displaystyle \sec^2{x} - \tan^2{x} \equiv 1$ ...

**beebe** · October 5th 2011, 07:01 PM

Thanks guys.

Originally Posted by TKHunny

Have you considered factoring out sec(x) from the numerator?

I feel kinda dumb for missing this one.

**Deveno** · October 5th 2011, 07:01 PM

Originally Posted by beebe

This might be more of a trig question, so if it is would someone kindly move it for me?

So I'm finding the second derivative of $ln[sec(x)+tan(x)]$ . My first derivative is $\frac{sec(x)tan(x)+sec^2(x)}{sec(x)+tan(x)}$ .

My question is: can I simplify this fraction to make taking the second derivative less tedious? I'm capable of doing it without simplifying first, but I don't want to get a super long and ugly answer.

yes.

Thread: Simplifying a denominator before taking derivative

LinkBack

Thread Tools

Display

Simplifying a denominator before taking derivative

Re: Simplifying a denominator before taking derivative

Re: Simplifying a denominator before taking derivative

Re: Simplifying a denominator before taking derivative

Re: Simplifying a denominator before taking derivative

Similar Math Help Forum Discussions

Rationalising surd/simplifying denominator

Taking The Derivative

Where am i going wrong on taking the derivative?

Taking a derivative

Taking the partial derivative

Search Tags