Find the derivative of the arctangent of x function

y = arctan(x)Start by taking the tangent of both sides:tan(y) = xTake the derivative of each side with respect to x, using implicit differentiation/the chain rule for the LHS, then rearrange to make dy/dx the subject:dy/dx = 1/sec^2(y)Use sec^2(y) = 1 + tan^2(y) to change the denominator:dy/dx = 1/(1 + tan^2(y))Plugging our original definition of y into this we get our final result:dy/dx = 1/(1 + tan^2(arctan(x))) = 1/(1 + x^2)

MB
Answered by Mitchell B. Further Mathematics tutor

1929 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

The point D has polar coordinates ( 6, 3π/4). Find the Cartesian coordinates of D.


How do you invert a 2x2 matrix?


Using graphs, show how the Taylor expansion can be used to approximate a trigonometric function.


Given that the quadratic equation x^2 + 7x + 13 = 0 has roots a and b, find the value of a+b and ab.


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