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
3004 Views
See similar Further Mathematics A Level tutorsRelated Further Mathematics A Level answers
All answers ▸How do I solve a simultaneous equation with more unknowns than equations?
I'm struggling with an FP2 First-Order Differential Equations Question (Edexcel June 2009 Q3) and the topic in general!
Two planes have eqns r.(3i – 4j + 2k) = 5 and r = λ (2i + j + 5k) + μ(i – j – 2k), where λ and μ are scalar parameters. Find the acute angle between the planes, giving your answer to the nearest degree.
A spring with a spring constant k is connected to the ceiling. First a weight of mass m is connected to the spring. Deduce the new equilibrium position of the spring, find its equation of motion and hence deduce its frequency f.