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)

Related Further Mathematics A Level answers

All answers ▸

In simple harmonic motion, where would the object have the largest speed. If the angular velocity is 2 rad s^-1, and the amplitude is 1m, what is the largest speed obtained by the object?


Show that cosh^2(x)-sinh^2(x)=1


Particles P and Q move in a plane with constant velocities. At time t = 0 the position vectors of P and Q, relative to a fixed point O in the plane, are (16i - 12j) m and -5i + 4j) m respectively. The velocity of P is (i + 2j) m/s and the velocity of Q


Prove by induction that 6^n + 4 is divisible by 5 for all integers n >= 1


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences