- #1
deancodemo
- 20
- 0
Homework Statement
Find [tex]\frac{d}{dx} \sin^{-1}(\sin x)[/tex]
Homework Equations
The Attempt at a Solution
Now, I know that the above expression simplifies directly to [tex]\frac{d}{dx} x = 1[/tex], but I attempted it the long way. Here it is:
[tex]\frac{d}{dx} \sin^{-1}(\sin x)[/tex]
[tex]= \frac{\cos x}{\sqrt{1 - \sin^2 x}}[/tex]
[tex]= \frac{\cos x}{\sqrt{\cos^2 x}}[/tex]
[tex]= \frac{\cos x}{|\cos x|}[/tex]
[tex]= 1 \mbox{ if } \cos x > 0[/tex]
[tex]= -1 \mbox{ if } \cos x < 0[/tex]
I know that this is incorrect! The answer should be 1. Did I incorrectly use the definition of [tex]\sqrt{x^2} = |x|[/tex]?