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

114166 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

Find the general solution to the differential equation; y'' + 4y' = 24x^2


Differentiate arctan(x) with respect to x


I do not understand this topic and particularly this example. In the class the result was found out but I still do not get it. How did the teacher came up with this outcome?


How to integrate ln(x)?


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