Prove that the derivative of tan(x) is sec^2(x).

Let y = tan(x)

Recall the definition of tan(x) as sin(x)/cos(x)

Therefore y = sin(x)/cos(x)

Use the quotient rule, which states that for y = f(x)/g(x), dy/dx = (f'(x)g(x) - f(x)g'(x))/g2(x) with f(x) = sin(x) and g(x) = cos(x).

Recall the derivatives of sin(x) as cos(x) and cos(x) as -sin(x)

This gives:

dy/dx = (cos(x)*cos(x) + sin(x)*sin(x)) / cos2(x)

Recall the trigonometric identity sin2(x) + cos2(x) = 1

Therefore dy/dx = 1/cos2(x) = sec2(x)

QED

Answered by Miriam G. Maths tutor

101356 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

A circle with centre C has equation x^2+8x+y^2-12y=12. The points P and Q lie on the circle. The origin is the midpoint of the chord PQ. Show that PQ has length nsqrt(3) , where n is an integer.


Write down the values of (1) loga(a) and (2) loga(a^3) [(1) log base a, of a (2) log base a of (a^3)]


If I have the equation of a curve, how do I find its stationary points?


How would you find the minimum turning point of the function y = x^3 + 2x^2 - 4x + 10


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