MYTUTOR SUBJECT ANSWERS

626 views

A curve has the equation (x+y)^2 = xy^2. Find the gradient of the curve at the point where x=1

The first step is to find dy/dx.

To do this you must first expand the brackets.

x2 + y2 + 2xy = xy2

Then differentiate each term with respect to x.

dy/dx of (x2) = 2x

dy/dx of (y2) = 2y(dy/dx)

(Using the product rule with u=yand v=1) this can be explained in more detail if necessary.

dy/dx of (2xy) = 2y + 2x(dy/dx)

(Also using the product rule with u=2x and v=y)

dy/dx of (xy2) = y2 + 2xy(dy/dx)

(Also product rule with u=x and v=y2)

Overall that gives:

2x + 2y + 2x(dy/dx) + 2y(dy/dx) = y2 + 2xy(dy/dx)

Then put all the terms containing (dy/dx) on the left and the others on the right.

This gives:

2x(dy/dx) + 2y(dy/dx) - 2xy(dy/dx) = y- 2x - 2y

This equals:

(dy/dx)(2x + 2y - 2xy) = y2 - 2x - 2y

Therefore:

(dy/dx) = (y2 - 2x - 2y) / (2x + 2y - 2xy)

From the original equation you now need to work at y at the point when x=1.

(1+y)2 = 1y2

y2 + 2y + 1 = y2

This is the same as:

2y + 1 = 0

2y = -1

y= -0.5

Substitute this into (dy/dx)

This gives:

[(-0.5)2 - 2(1) -2(-0.5)] / [2(1) + 2(-0.5) - 2(1 x -0.5)]

This equals

(0.25 - 2 + 1) / (2 - 1 +1)

Therefore the gradient equals -3/8

Motunrayo O. A Level Biology tutor, GCSE Biology tutor, IB Biology tu...

12 months ago

Answered by Motunrayo, an A Level Maths tutor with MyTutor


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

347 SUBJECT SPECIALISTS

PremiumTimothy N. A Level Design & Technology tutor, GCSE Design & Technolog...
£36 /hr

Timothy N.

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

Subjects offered:Maths, Physics+ 2 more

Maths
Physics
Design & Technology
-Personal Statements-

“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!”

Roma V. A Level Maths tutor, 13 Plus  Maths tutor, GCSE Maths tutor, ...
£26 /hr

Roma V.

Degree: Mathematics, Operational Research, Statistics and Economics (Bachelors) - Warwick University

Subjects offered:Maths, Further Mathematics + 1 more

Maths
Further Mathematics
Economics

“Top tutor from the renowned Russell university group, ready to help you improve your grades.”

PremiumGeorge B. GCSE Maths tutor, A Level Maths tutor, A Level Further Math...
£26 /hr

George B.

Degree: Mathematics (Masters) - Warwick University

Subjects offered:Maths, Further Mathematics + 1 more

Maths
Further Mathematics
.STEP.

“Premium tutor. First class graduate with teaching experience from a top Russell Group university. I deliver fun and relaxed lessons which achieve results!”

About the author

£20 /hr

Motunrayo O.

Degree: Medicine (Bachelors) - Manchester University

Subjects offered:Maths, Science+ 7 more

Maths
Science
Physics
Chemistry
Biology
.UKCAT.
.BMAT (BioMedical Admissions)
-Personal Statements-
-Medical School Preparation-

“Top tutor from the renowned Russell university group, ready to help you improve your grades.”

MyTutor guarantee

You may also like...

Posts by Motunrayo

A curve has the equation (x+y)^2 = xy^2. Find the gradient of the curve at the point where x=1

Which are the most GCSE heavy universities?

Other A Level Maths questions

Differentiate the equation y = (1+x^2)^3 with respect to (w.r.t.) x using the chain rule. (Find dy/dx)

How would you solve (2x+16)/(x+6)(x+7) in partial fractions?

What is the gradient of y = xcos(x) at x=0?

Explain how Differentiation by the chain rule works

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