MYTUTOR SUBJECT ANSWERS

824 views

x^2 + y^2 + 10x + 2y - 4xy = 10. Find dy/dx in terms of x and y, fully simplifying your answer.

x2 + y2 + 10x + 2y - 4xy = 10

Start by differentiating both sides by x, the terms not containing y are differentiated normally, x2 becomes 2x, 10x becomes 10, and 10 becomes 0.
For the y2 term, by implicit differentiation the result is 2y (the same as with x) multiplied by a factor of dy/dx, or 2y(dy/dx).
For the 2y term, as above, the result is the same as for x, 2 in this case, multiplied by a factor of dy/dx. I.e. 2(dy/dx).
The -4xy term requires use of the product rule (d(uv)/dx = v(du/dx) + u(dv/dx)). In this case that gives d(-4xy)/dx = -4x(dy/dx) + y(-4). 
Our completely differentiated equation is now
2x + 2y(dy/dx) + 10 + 2(dy/dx) -4x(dy/dx) - 4y = 0
Grouping the dy/dx terms and taking the remaining terms to the other side gives
(2y + 2 - 4x)(dy/dx) = 4y - 10 - 2x
Dividing through by (2y + 2 - 4x) gives
(dy/dx) = (4y - 10 - 2x)/(2y + 2 - 4x)
Simplifying the fraction on the Right Hand Side gives
(dy/dx) = (2y - 5 - x)/(y + 1 - 2x)

Guy L. A Level Further Mathematics  tutor, A Level Maths tutor, A Lev...

1 year ago

Answered by Guy, who tutored A Level Maths with MyTutor


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

262 SUBJECT SPECIALISTS

£24 /hr

Sam H.

Degree: Computer Science (Masters) - Warwick University

Subjects offered: Maths, Physics+ 1 more

Maths
Physics
Chemistry

“Second year Computer Scientist at the University of Warwick, here to help you perform to your best in your exams!”

MyTutor guarantee

£20 /hr

Leo P.

Degree: Theoretical Physics (Masters) - University College London University

Subjects offered: Maths, Further Mathematics

Maths
Further Mathematics

“About Me: I am a MSci Theoritical Physics student at University College London (UCL). Maths is everywhere and that's what I love about maths. Hopefully you'll enjoy it too I am a friendly, understanding and patient tutor that enjoys t...”

MyTutor guarantee

£20 /hr

Killian D.

Degree: Mathematics (Bachelors) - Edinburgh University

Subjects offered: Maths, Physics+ 1 more

Maths
Physics
.MAT.

“Who am I? I am a first year Mathematics student in the University of Edinburgh. I am studying full time but have chosen to tutor as well as I have a passion for the subject; something I believe you will discover for yourself in our tu...”

MyTutor guarantee

About the author

Guy L.

Currently unavailable: for new students

Degree: Mathematics (Masters) - Bristol University

Subjects offered: Maths, Physics+ 1 more

Maths
Physics
Further Mathematics

“About Me I am a Maths student at Bristol University with a keen interest in learning everything about science! I have tutored at several different ability and qualification levels over the past few years and have always received posit...”

You may also like...

Posts by Guy

Paul travels from Rye to Eston at an average speed of 90 km/h. He travels for T hours. Mary makes the same journey at an average speed of 70 km/h. She travels for 1 hour longer than Paul. Work out the value of T

x^2 + y^2 + 10x + 2y - 4xy = 10. Find dy/dx in terms of x and y, fully simplifying your answer.

Other A Level Maths questions

Differentiate x^2

differentiate y=(4x^3)-5/x^2

How do you find the minimum of the equation sin^2(x) + 4sin(x)?

Integrate this funtion f'(x)=2x +4 with respect to x (C1 integration)

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