Prove that the d(tan(x))/dx is equal to sec^2(x).

MYTUTOR SUBJECT ANSWERS

Answers / Maths / A Level / Prove that the d(tan(x))/dx is equal to sec^2(x).

637 views

Prove that the d(tan(x))/dx is equal to sec^2(x).

You can express tan(x) as sin(x)/cos(x).

Therefore, tan(x)= sin(x)/ cos(x)

The quotient rule can be applied here as there is a function of x in the numerator and denominator.

Quotient Rule: (v*(du/dx) - u*(dv/dx))/v²

Let u =sin(x) and v=cos(x) and hence (du/dx)= cos(x) and (dv/dx)= -sin(x).

Therefore:

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

=(cos²(x)+sin²(x))/(cos²(x))

Using the trig identity, cos²(x)+sin²(x)=1, the numerator of the fraction can be tidied and heavily simplified.

d(tan(x))/dx= 1/(cos²(x))

As 1/(cos(x)) is equal to sec(x), 1/(cos²(x)) is equal to sec²(x).

Chinazam U. GCSE Maths tutor, 11 Plus Maths tutor, A Level Maths tuto...

9 months ago

Answered by Chinazam, an A Level Maths tutor with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist

335 SUBJECT SPECIALISTS

View profile

£30 /hr

Rachel H.

Degree: Physics and Astronomy with a Year Abroad (Bachelors) - Durham University

Subjects offered:Maths, Science+ 3 more

“Hey, I'm Rachel and I'm Physics graduate from Durham University. My best subjects at school were always science and maths but I also loved languages and art”

4.8

51 reviews | 135 completed tutorials

Save profile

£36 /hr

Timothy N.

Degree: Architecture and Environmental Engineering (Masters) - Nottingham University

Subjects offered:Maths, Physics+ 2 more

“Hi there, I have a passion for helping students achieve, and believe that with my 200+ hours of experience, we will be able to surpass the grades you want!”

5.0

117 reviews | 247 completed tutorials

Save profile

£30 /hr

Shruti V.

Degree: Biomedical Engineering (Masters) - Southampton University

Subjects offered:Maths, Physics+ 2 more

“I am patient and friendly and strive for a comfortable and fun working environment that also achieves results.”

5.0

69 reviews | 171 completed tutorials

Save profile

See more A Level Maths tutors

About the author

View profile

Chinazam U.

Currently unavailable: until 01/02/2017

Degree: MEng in Materials Engineering with International Study (Masters) - Exeter University

Subjects offered:Maths, Further Mathematics

“I am a Materials Engineering student at the University of Exeter. I enjoy mathematical-based subjects the most of all the subjects which I have learnt over the years, and I hope that I can help to further your understanding in all are...”

MyTutor guarantee

Save profile

Version:	3.48.0
Build:	c981a57a9cf4
Time:	2017-07-24T15:36:26Z

MYTUTOR SUBJECT ANSWERS

Prove that the d(tan(x))/dx is equal to sec^2(x).

Still stuck? Get one-to-one help from a personally interviewed subject specialist

335 SUBJECT SPECIALISTS

About the author

You may also like...

Other A Level Maths questions

One-to-one help is at your fingertips