Why is the derivative of inverse tan(x) 1/(1+x^2)?
This can be proven by understanding tan(x) and it's inverse as functions, using implicit differentiation, subsitution and by recognising trigonometric identities (or being able to prove them from first principles). Once this is learned, the same can be repeated for the inverse of other trigonometric functions. I have drafted a proof which can be seen in the Online Lesson Space.
NG
Related Maths A Level answers
All answers ▸How to find the stationary point of y= x^2-108x^(1/2)+16 and determine the nature of the stationary point?
What is the tangent line to the curve y = x^3+4x+5 at the point where x = 2?
When do I use the chain rule and when do I use the product rule in differentiation?
In a science experiment a substance is decaying exponentially. Its mass, M grams, at time t minutes is given by M=300e^(-0.05t). Find the time taken for the mass to decrease to half of its original value.