Calculus Possible typo at "Cálculo", by Robert A. Adams

[mcastillo356]

Hi PF

I've got the 6th Spanish edition of "Calculus", by Robert A. Adams. At the chapter 3.5, "Inverse trigonometric functions", few lines below "Definition 12 The inverse function of cosine cos^-1x or arccos x ", it says:
"The derivative of cos^-1x is the negative of that of sin^-1x (why?):

$$\dfrac{d}{dx}\cos^{-1}x=\dfrac{1}{\sqrt{1-x^2}}$$

This last is a typo; there is a minus sign forgotten, isn't it?

Greetings

 

[Baluncore]

The 6th Spanish edition of "Calculus" is wrong.
https://en.wikipedia.org/wiki/Inver...erivatives_of_inverse_trigonometric_functions

 

[PeroK]

"The derivative of cos^-1x is the negative of that of sin^-1x (why?):

Look at the graphs on this page:

https://mathworld.wolfram.com/InverseTrigonometricFunctions.html

Also, note that: $$\sin^{-1}x + \cos^{-1}x = \frac \pi 2$$