New Help, Cannot Seem to Get it

[alexparker]

Prove that (d/dx)arcos(x) = -1/(Sqrt(1-x^2)

Homework Equations

The Attempt at a Solution

 

[Dick]

cos is the inverse function of arccos. So cos(arccos(x))=x. Differentiate both sides. Did you try that?

 

[HallsofIvy]

Or: if y= arccos(x) then x= cos(y). Differentiate that to find dx/dy= -sin(y) so that
dy/dx= -1/sin(y)= -1/sin(arccos(y)).

Use trig identities to simplify that (change sin(arccos(y)) to cos(arccos(y))=y) or think about a right triangle with "near side" of length y and hypotenuse of length 1. What is the length of the "opposite side"? Whatr is the sine?