How do you calculate the derivative of cos inverse x?

When differentiating cos inverse x, the typical method is to make y equal to cos inverse x.By taking cos of both sides: x = cosy.You can then differentiate with respect to y, obtaining that: (dx/dy) = - sinyUsing our knowledge of derivatives, we now know that: (dy/dx) = -1/(siny)From x = cosy, x^2 = (cosy)^2                  = 1 - (siny)^2          (siny)^2 = 1 - x^2            siny = (1-x^2)^(1/2)Combining this with the equation stating (dy/dx), we get:     (dy/dx) = (-1)/((1-x^2)^(1/2))Since y is equal to the cos inverse function, this is now equal to the derivative of cos inverse x.

WW
Answered by Will W. Further Mathematics tutor

6623 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

The plane Π contains the points (1, 2, 3), (0, 1, 2) and (2, 3, 0). What is the vector equation of the plane? and what is the cartesian equation of the plane?


Give the general solution to (d2y/dx2) - 2dy/dx -3y = 2sinx


Solve the second order differential equation d^2y/dx^2 - 4dy/dx + 5y = 15cos(x), given that when x = 0, y = 1 and when x = 0, dy/dx = 0


How do you calculate the cross product of two vectors?


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning