How do I differentiate tan(x) ?

To differentiate tan(x):

Note: Here, we use d/dx f(x) to mean "the derivative of f(x) with respect to x". 

1) rewrite tan(x) as sin(x)/cos(x)

2) Apply the quotient rule (or, alternatively, you could use the product rule using functions sin(x) and 1/cos(x)):

Using the quotient rule:

d/dx tan(x) = (cos(x)cos(x) - sin(x)(-sin(x))) / cos2(x)

d/dx tan(x) = (cos2(x) + sin2(x)) / cos2(x)

3) Recall/Note the following identity: cos2(x) + sin2(x) = 1

So, d/dx tan(x) = 1 / cos2(x)

4) Use the definition of sec(x):

So, d/dx tan(x) = sec2(x), as required 

 

JH
Answered by Joseph H. Further Mathematics tutor

125624 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

Show that the square of any odd integer is of the form (8k+1)


Prove that (AB)^-1 = B^-1 A^-1


The infinite series C and S are defined C = a*cos(x) + a^2*cos(2x) + a^3*cos(3x) + ..., and S = a*sin(x) + a^2*sin(2x) + a^3*sin(3x) + ... where a is a real number and |a| < 1. By considering C+iS, show that S = a*sin(x)/(1 - 2a*cos(x) + a^2), and find C.


How to integrate ln(x)?


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences