Differentiate w.r.t x the expression arccos(x).

Using implicit differentiation, let y equal arccos(x) : y=arccos(x). So x = cos(y), and dx/dy = -sin(y). dy/dx is therefore -1/sin(y). from trig indentities: sin(y) = sqrt(1-cos^2(y)). Substituting gives dy/dx = -1/sqrt(cos^2(y)) which is the derivative of arccos.

DP
Answered by Daniel P. Further Mathematics tutor

3014 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

How do I prove that the differential of coshx is equal to sinhx?


Prove that ∑(1/(r^2 -1)) from r=2 to r=n is equal to (3n^2-n-2)/(4n(n+1)) for all natural numbers n>=2.


Find the area of the surface generated when the curve with equation y=cosh(x) is rotated through 2 pi radians about the x axis, with 2<=x<=6


A rectangular hyperbola has parametric equations x = 4t, y = 4/t , (z non 0). Points P and Q on this hyperbola have parameters t = 1/4 and t = 2. Find the equation of the line l which passes through the origin and is perpendicular to the line PQ.


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