MYTUTOR SUBJECT ANSWERS

478 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...

7 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

269 SUBJECT SPECIALISTS

£36 /hr

James G.

Degree: Mathematical Physics (Doctorate) - Nottingham University

Subjects offered:Maths, Physics+ 2 more

Maths
Physics
Further Mathematics
.STEP.

“Currently a 3rd year PhD student in Mathematical Physics. I'm very passionate about teaching as well as my subject area. Look forward to hearing from you.”

£22 /hr

Laura L.

Degree: Chemistry (MCHEM) (Masters) - Warwick University

Subjects offered:Maths, Chemistry+ 1 more

Maths
Chemistry
Biology

“Hi there! I'm a third-year Chemistry student, I tutor maths from 11+ to A level as well as GCSE Science, A level Biology, and Chemistry”

£30 /hr

Michelangelo M.

Degree: MMath Mathematics with Placement (Masters) - Bath University

Subjects offered:Maths, Italian+ 4 more

Maths
Italian
Further Mathematics
Computing
.STEP.
.MAT.

“Mathematics student at the University of Bath, willing to help you love this subject and improve your grades.”

About the author

Chinazam U.

Currently unavailable: until 01/02/2017

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

Subjects offered:Maths, Further Mathematics

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

You may also like...

Other A Level Maths questions

How do you find the area between two lines?

How do you differentiate 2 to the power x?

What does differentiation actually mean?

How do you find the integral of sin^2(x) dx?

View A Level Maths tutors

We use cookies to improve your site experience. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok