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

2095 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

Using the substitution u = ln(x), find the general solution of the differential equation y = x^2*(d^2(y)/dx^2) + x(dy/dx) + y = 0


A curve has the equation (5-4x)/(1+x)


Differentiate arctan of x with respect to x.


Find the inverse of a 3x3 matrix


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