How do you derive y=tanx using the definition of the derivative?
February 20th, 2023
Use the tangent of a sum, continuity of tangent and ##lim_(hrarr0)tan h/h = 1##
##f(x) = tanx##
##f'(x) = lim_(hrarr0)(tan(x+h) – tanx)/h##
## = lim_(hrarr0)((tanx+tan h)/(1-tanxtan h) – tanx)/h##
## = lim_(hrarr0)(tanx+tan h- tanx+tan^2xtan h)/(h(1-tanxtan h)) ##
## = lim_(hrarr0)(tan h/h * (1+tan^2x)/(1-tanxtan h)) ##
## = (1) * (1+tan^2x)/(1-0) = 1+tan^2x = sec^2x##
