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

6447 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

A block of mass 50kg resting on a rough surface with a coefficient of friction equal to 1/3. Find the maximum angle at which the surface can be inclined to the horizontal without the block slipping. Give your answer to 3 significant figures


How do you prove by induction?


If the complex number z = 5 + 4i, work out 1/z.


The quadratic equation x^2-6x+14=0 has roots alpha and beta. a) Write down the value of alpha+beta and the value of alpha*beta. b) Find a quadratic equation, with integer coefficients which has roots alpha/beta and beta/alpha.


We're here to help

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

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences