Need help to find dx/dy

Question

Given that x = 3/(y-2), find dx/dy

Thanks for the help.

Question

Given that x = 3/(y-2), find dx/dy

Thanks for the help.

take out '3' as it's a constant.

let u = y - 2

du/dy = 1

x = 1/ u

3 dx/du = 3 ln u

therefore dx/ dy = 3 ln (y-2)

use e chain rule

dx/ dy = dx/ du du/dy

take out '3' as it's a constant.

let u = y - 2

du/dy = 1

x = 1/ u

3 dx/du = 3 ln u

therefore dx/ dy = 3 ln (y-2)

I will suggest something else instead.

x=3/(y-2)

dx/dy

= [-3/(y-2)^2][d/dy (y-2)]

= [-3/(y-2)^2](1)

= -3/(y-2)^2

What level are you at?

If A levels H2 Maths, one should be able to jump direct to the answer in one step.

If O levels or H1 Maths, then the easiest wat is to change to 3(y-2)^-1, and differentiate using chain rule

What level are you at?

If A levels H2 Maths, one should be able to jump direct to the answer in one step.

If O levels or H1 Maths, then the easiest wat is to change to 3(y-2)^-1, and differentiate using chain rule

How to jump in H2 maths, using formulae? MF15?

It should already be familiar that differentiating 1/x w.r.t. x gives -1/x^2

Hence, differentiating 3/(y-2) w.r.t. y will immediately gives us -3/(y-2)^2

This is what I expect of my H2 maths students.