# Simplifying a Derivative

1. Jul 15, 2012

### communitycoll

1. The problem statement, all variables and given/known data
Find derivative of sin^-1 (2x + 1)

2. Relevant equations
I do everything Wolfram does except I don't know how to simplify to get the final answer.

http://www.wolframalpha.com/input/?i=derivative+sin^-1+(2x+++1)

3. The attempt at a solution
Everything Wolfram does basically.

2. Jul 15, 2012

### HallsofIvy

Staff Emeritus
I don't see how you can expect anyone to tell you how to simplify what you got to Wolfram's formula, if you don't tell us what you got!

3. Jul 15, 2012

### communitycoll

Ah terribly sorry. 2 / sqrt(1 - (2x + 1)^2); the last thing in the show steps part for the derivative in Wolfram.

4. Jul 15, 2012

### HallsofIvy

Staff Emeritus
Of course, you know that (2x+1)^2= 4x^2+ 4x+ 1. That means 1- (2x+1)^2= 1 -4x^2- 4x- 1= -4x^2- 4x= -4(x^2- x)= -4x(x-1).

5. Jul 15, 2012

### communitycoll

But if -4x(x-1) is under a radical (as well as being multiplied) how is it that I pull a 2 out of that?

6. Jul 15, 2012

### QED Andrew

$\sqrt{-4x(x-1)} = \sqrt{4 \cdot -x(x-1)} = \sqrt{4} \sqrt{-x(x-1)} = 2\sqrt{-x(x-1)}$

It should be noted $1 - (2x + 1)^2 = -4x(x+1)$. I'll leave it to you to show $\sqrt{-4x(x+1)} = 2\sqrt{-x(x+1)}$.

Last edited: Jul 15, 2012
7. Jul 15, 2012

### HallsofIvy

Staff Emeritus
What, exactly, do you think the square root of 4 is?

8. Jul 15, 2012

### communitycoll

Ah. I understand now. It took me a bit, but I understand now. Thanks.