How do you derive y=tanx using the definition of the derivative?
1 Answer
Sep 6, 2015
Use the tangent of a sum, continuity of tangent and
Explanation:
# = 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#
