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...

2 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


Evan J. GCSE Maths tutor, A Level Maths tutor, A Level Further Mathem...
View profile
£20 /hr

Evan J.

Degree: Mathematics (Masters) - Exeter University

Subjects offered: Maths, Further Mathematics

Further Mathematics

“I am a patient individual who is willing to try various approaches to the content”

MyTutor guarantee

Julia C. GCSE Chemistry tutor, A Level Chemistry tutor, 13 plus  Math...
View profile
£20 /hr

Julia C.

Degree: Chemical Engineering (Masters) - Birmingham University

Subjects offered: Maths, Physics+ 2 more

-Personal Statements-

“About Me: I am a 3rd year Chemical Engineering student with a strong background in the STEM subjects.  I am a tutor with almost 4 years' experience of working with a range of different students. Every student learns differently and e...”

Elakkeya J. A Level Biology tutor, GCSE Biology tutor, GCSE Chemistry...
View profile
£22 /hr

Elakkeya J.

Degree: Chemical Engineering (Masters) - Sheffield University

Subjects offered: Maths, Science+ 2 more


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

About the author

Graham R. A Level Maths tutor, GCSE Maths tutor, A Level Physics tuto...
View profile
£20 /hr

Graham R.

Degree: Geophysics with Geology (Bachelors) - Durham University

Subjects offered: Maths, Physics+ 1 more


“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

Polynomial long division, how do I do it?

How to differentiate x^2 + y^2 - 2x + 6y = 5

Find the sum and product of the roots of the equation 2x^2+3x-5=0

For what values of k does the graph y=x^(2)+2kx+5 not intersect the x-axis

View A Level Maths tutors


We use cookies to improve our service. By continuing to use this website, we'll assume that you're OK with this. Dismiss