MYTUTOR SUBJECT ANSWERS

350 views

Find the exact gradient of the curve y=ln(1-cos2x) at the point with x-coordinate π/6

This is a past paper question for an A level OCR MEI paper for Maths.

We need to find the gradient of the curve so we know right away that we need to use differentiation.

The equation y = ln(1-cos2x) is difficult to differentiate by itself so we use the chain rule and a substitution. We say y = ln(u) where u = 1-cos2x.

dy/du = 1/u. This is something you just have to learn, that the differential of y= lnx is 1/x.

If you're stuck with finding du/dx, you can use another substitution if you want where u = 1-cosv and v = 2x, but most people know (after a lot of practice) that the differential of y=coskx is -ksinkx. I believe it's also in most formula books.

So here du/dx = -2sin2x (remember the change of sign when going from cos to sin when differentiating).

So from the chain rule, we know that dy/dx = dy/du x du/dx so dy/dx = 1/u x -2sin2x = -2sin2x/u and u = 1-cos2x so dy/dx = -2sin2x/(1-cos2x)

Now we need to find the value of this gradient when x = π/6

dy/dx = -2sin2x/(1-cos2x) = -2sin(2 x π/6)/(1-cos(2 x π/6)) = -2sin(π/3)/(1-cos(π/3)) 

Remember that we're working in radians here so for this, you need to put your calculator in radians too

We know that cos(π/3) = 1/2 (or 0.5, but 1/2 is easier for the moment) and sin(π/3) = root(3)/2

So dy/dx at x=π/3 gives (-2 x root(3)/2)/(1-1/2) => multiply top and bottom by 2 => -2root(3)/(2-1) = -2root(3)/1 = -2root(3)

Catherine H. A Level Physics tutor, GCSE Chemistry tutor, GCSE Biolog...

10 months ago

Answered by Catherine, an A Level Maths tutor with MyTutor

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

183 SUBJECT SPECIALISTS

£22 /hr

Kirsty S.

Degree: Mathematics (Bachelors) - Warwick University

Subjects offered: Maths, Spanish+ 1 more

Maths
Spanish
Further Mathematics

“Hello, I'm Kirsty and I am here to help you with Maths. Maths will soon become the exam that you will look forward to, so you can show off how much you know! Before I begin any tuition I find out exactly what you would like to get ou...”

£20 /hr

Henry T.

Degree: Economics (Bachelors) - Leeds University

Subjects offered: Maths, Economics

Maths
Economics

“About me: I am a 20 year old third year economics student, currently achieving a first class degree at the Univesity of Leeds. Economics and Maths are two subjects that genuinely excite me. My degree allows me to study economics but al...”

MyTutor guarantee

£20 /hr

William D.

Degree: Mechanical Engineering (Masters) - Leeds University

Subjects offered: Maths, Physics+ 2 more

Maths
Physics
Italian
Chemistry

“I am a British student currently in the first year of a masters degree in Mechanical Engineering at the University of Leeds. Having previously lived in Spain and Italy, I am fluent in both languages and have excellent communications s...”

MyTutor guarantee

About the author

Catherine H.

Currently unavailable: for regular students

Degree: Physics with Astrophysics (MSci) (Masters) - Bath University

Subjects offered: Maths, Physics+ 4 more

Maths
Physics
Further Mathematics
French
Chemistry
Biology

“Hi there! My name's Catherine. I am a first year student at the University of Bath studying Physics and Astrophysics. I spent a year at UPMC, a university in Paris between my A levels and coming to Bath, studying Physics, Chemistry, M...”

You may also like...

Posts by Catherine

Find the exact gradient of the curve y=ln(1-cos2x) at the point with x-coordinate π/6

The speed of water moving through a turbine is 2.5 m/s. Show that the mass of water passing through an area of 500 metres squared in one second is about 1 x 10^6 kg (density of sea water = 1030 kg/m^3)

Other A Level Maths questions

How does integration work?

why does log a + log b = log (ab)

What is a logarithm?

How can we determine stationary points by completing the square?

View A Level Maths tutors

Cookies:

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

mtw:mercury1:status:ok