529 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)

10 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

#### 303 SUBJECT SPECIALISTS

£36 /hr

Ignacio P.

Degree: Aerospace Engineering MEng (Masters) - Bristol University

Subjects offered:Maths, Spanish+ 5 more

Maths
Spanish
Science
Physics
Further Mathematics
Chemistry
-Personal Statements-

“Author of The 3-Step Method to Achieving (under publishing) - APPLIED NEUROSCIENCE & COACHING FOR EXPLOSIVE RESULTS IN MATH, PHYSICS, SPANISH & MORE!”

£22 /hr

Max G.

Degree: Mathematics and Physics (Masters) - Durham University

Subjects offered:Maths, Physics+ 1 more

Maths
Physics
Further Mathematics

“I am a maths and physics student at the University of Durham, for as long as I can remember i have been obsessed with all things science! I am patient, friendly and most of all understanding to the fact that the sciences aren't for ev...”

£20 /hr

Lucy S.

Degree: Chemistry (Masters) - Durham University

Subjects offered:Maths, Chemistry

Maths
Chemistry

“Reading Chemistry at Durham University with expertise in Chemistry and Mathematics (A*A*) at GCSE/A-level”

£20 /hr

Motunrayo O.

Degree: Medicine (Bachelors) - Manchester University

Subjects offered:Maths, Science+ 7 more

Maths
Science
Physics
Chemistry
Biology
.UKCAT.
-Personal Statements-
-Medical School Preparation-

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

What is the differential of e^x?

Find the x co-ordinates of the stationary points of the graph with equation y = cos(x)7e^(x). Give your answer in the form x = a +/- bn where a/b are numbers to be found, and n is the set of integers.

What is differentiation and why is it useful?

Differentiate y=sin(x)/5x^3 with respect to x

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