Show that the derivative of tan(x) is sec^2(x), where sec(x) is defined as 1/cos(x). [Hint: think of tan(x) as a quotient of two related functions and apply the appropriate identity]

tan(x) is defined as sin(x)/cos(x) For a function which can be written as f(x) = u(x)/v(x) the quotient rule can be appliedThe quotient rule states f ' (x) = (u'v-v'u)/v^2 Applying this to the formula for tan we obtain ( cos(x)cos(x) - (-sin(x)sin(x))/(cos(x)^2)Examining the numerator the minus's cancel and we obtain sin(x)^2+cos(x)^2 by a quotable identity this always equals 1Hence the expression simplifies to 1/cos(x)^2 = sec^2(x) as originally statedHence shown.

Answered by Oliver C. Maths tutor

2876 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Differentiate y= (6x^2 - 5)^(3/2) with respect to x


Let f(x) = x^3 -2x^2-29x-42. a)Show (x+2) is a factor b)Factorise f(x) completely


Why is it that the sum of all natural numbers up to n is 1/2(n)(n+1)?


What is an integral?


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