MYTUTOR SUBJECT ANSWERS

267 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...

5 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

296 SUBJECT SPECIALISTS

£20 /hr

Nigel M.

Degree: Economics and maths (Bachelors) - Bath University

Subjects offered:Maths, Physics+ 2 more

Maths
Physics
Further Mathematics
-Personal Statements-

“First year Economics and Maths student here to help you out with A-level or GCSE maths and physics!”

MyTutor guarantee

£20 /hr

Rahul P.

Degree: Economics (Bachelors) - LSE University

Subjects offered:Maths, Further Mathematics

Maths
Further Mathematics

“I'm enthusiastic about Maths and I think my 598/600 UMS in Maths A Level puts me in a strong position to help others.”

MyTutor guarantee

£20 /hr

Murray M.

Degree: Mathematics and Physics (Masters) - Bath University

Subjects offered:Maths, Physics

Maths
Physics

“About Me: I am a second year Maths and Physics student at the University of Bath. I have always been passionate about these subjects, in particular how they can explain so much of the world around us, and I hope to be able to share th...”

MyTutor guarantee

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 would I differentiate cos(2x)/x^1/2

What is the tangent line to the curve y = x^3+4x+5 at the point where x = 2?

Prove that the indefinite integral of I = int(exp(x).cos(x))dx is (1/2)exp(x).sin(x) + (1/2)exp(x).cos(x) + C

Given that 5cos^2(x) - cos(x) = sin^2(x), find the possible values of cos(x) using a suitable quadratic equation.

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