MYTUTOR SUBJECT ANSWERS

447 views

y = x*(x-2)^-1/2. Prove dy\dx = (x-4)/2*(x-2)^3/2

Firstly, when approaching a differentiation question you need to work out what method you need to use to solve it. As you can see there are two terms multiplied by one another (the 'x' term and the '(x-2)-1/2' term), therefore the product rule must be used. 

Making u = x and v = (x-2)-1/2

du/dx = 1 dv/dx = -1/2*(x-2)-3/2

Substituing these things into the Product Rule equation we get: 

dy/dx = -x/2*(x-2)-3/2 + (x-2)-1/2

Now we need to focus on manipulating this equation to match the one given in the question. To start with we will take out a factor of (x-2)-3/2 giving: 

dy/dx = (x-2)-3/2*(-x/2 + x-2) 

Simplyfying : 

dy/dx = (x-2)-3/2* (x/2 -2)

Multiplying by 2 : 

dy/dx = (x-4)/2*(x-2)3/2

Graham R. A Level Maths tutor, GCSE Maths tutor, A Level Physics tuto...

9 months ago

Answered by Graham, an A Level Maths tutor with MyTutor


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

269 SUBJECT SPECIALISTS

Timothy N. A Level Design & Technology tutor, GCSE Design & Technolog...
£26 /hr

Timothy N.

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

Subjects offered:Maths, Science+ 3 more

Maths
Science
Physics
Design & Technology
-Personal Statements-

“Hi there, I have a passion for helping students achieve, and believe that with my years of experience tutoring, we will be able to surpass the grades you want!”

£24 /hr

Runzhi C.

Degree: Medicine (Bachelors) - Imperial College London University

Subjects offered:Maths, Chemistry+ 3 more

Maths
Chemistry
Biology
-Personal Statements-
-Medical School Preparation-

“Hi there, I am an experienced tutor for Biology and Maths. A money-back guarantee is provided if you are not 100% happy with the session. ”

PremiumImogen W. GCSE Chemistry tutor, GCSE Maths tutor, A Level Chemistry t...
£30 /hr

Imogen W.

Degree: Chemistry (Masters) - University College London University

Subjects offered:Maths, Chemistry

Maths
Chemistry

“I am very enthusiastic and patient. I want my students to be able to understand their studies so that they can enjoy them as much as I do.”

About the author

Graham R. A Level Maths tutor, GCSE Maths tutor, A Level Physics tuto...

Graham R.

Currently unavailable: for new students

Degree: Geophysics with Geology (Bachelors) - Durham University

Subjects offered:Maths, Physics+ 1 more

Maths
Physics
Geography

“About Me I am a 3rd year Geophysics and Geology student at Durham University. Ever since I was small Maths seemed to click with me and I always found it easy to explain. These skills came in use when I was asked to be an academic ment...”

You may also like...

Posts by Graham

Using logarithms solve 8^(2x+1) = 24 (to 3dp)

y = x*(x-2)^-1/2. Prove dy\dx = (x-4)/2*(x-2)^3/2

Other A Level Maths questions

How to factorise any quadratic expression

How do we differentiate y = arctan(x)?

How do you intergrate sin^2(x)?

The first term of an infinite geometric series is 48. The ratio of the series is 0.6. (a) Find the third term of the series. (b) Find the sum to infinity. (c) The nth term of the series is u_n. Find the value of the sum from n=4 to infinity of u_n.

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