MYTUTOR SUBJECT ANSWERS

805 views

If x = cot(y) what is dy/dx?

Here we will use:

cot(x) = cos(x)/sin(x)

cosec2(x) = 1 + cot2(x)

Chain rule : dy/dt * dt/ dx = dy/ dx

Product rule : d/dx (u*v) = u*dv/dx + v*du/dx

x = cot(y)= cos(y)/sin(y)

dx/dy = -cos(y)*(cos(y)/sin(y)2) + 1/sin(y)* (-sin(y))

         = -cos2(y)/sin2(y) -1 = - cos2(y)/sin2(y) -sin2(y)​ /sin2(y)

         = -(sin2(y)+ cos2(y))/sin2(y)​ = -cosec2(y)

cosec2(y) = 1 + cot2(y)

x = cot(y)

dx/dy = -(1 + x2)

dy/dx = -1/(1+x2)

Sahiti S. GCSE Maths tutor, A Level Economics tutor, A Level Maths tutor

2 years ago

Answered by Sahiti, an A Level Maths tutor with MyTutor


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

183 SUBJECT SPECIALISTS

£20 /hr

Bradley P.

Degree: Medicine (Other) - Liverpool University

Subjects offered: Maths, Physics+ 3 more

Maths
Physics
Chemistry
Biology
-Medical School Preparation-

“About me: I am currently a 3rd year medical student who has always had a passion for teaching. I am a very patient and easy going person, and this helps when it comes to tutoring as it is you who can guide me in the direction of what ...”

MyTutor guarantee

£24 /hr

Barnaby W.

Degree: Mathematics (Masters) - Southampton University

Subjects offered: Maths, Further Mathematics

Maths
Further Mathematics

“ I have always enjoyed tutoring. I find that it gives me real satisfaction to see a child or student you have helped feel much more confident”

£20 /hr

Georgiana P.

Degree: Mathematics (Bachelors) - Bristol University

Subjects offered: Maths

Maths

“I am a Maths student at the University of Bristol and hope to share my love of maths with you. I believe that Maths is learnt in 3 steps:    1) I will explain and we will discuss the main principles of what we are working on, assis...”

About the author

Sahiti S.

Currently unavailable: for new students

Degree: Natural Sciences (Bachelors) - Durham University

Subjects offered: Maths, Economics

Maths
Economics

“Hi, my name is Sahiti and I am a second year natural sciences student (studying maths, economics and computer science).  Why me? I am passionate about both maths and economics, which both make up a major part of my degree. I l love t...”

You may also like...

Posts by Sahiti

How do you solve the simultaneous equations 3x + 4y = 5 and 2x – 3y = 9

If x = cot(y) what is dy/dx?

What is the Current Account

Other A Level Maths questions

What is the dot product of two vectors?

A rollercoaster stops at a point with GPE of 10kJ and then travels down a frictionless slope reaching a speed of 10 m/s at ground level. After this, what length of horizontal track (friction coefficient = 0.5) is needed to bring the rollercoaster to rest?

How can I differentiate x^2+2y=y^2+4 with respect to x?

Find the values of x, where 0 < x < 360, such that x solves the equation: 8(tan[x])^2 – 5(sec[x])^2 = 7 + 4sec[x]

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