How would you differentiate 1 over 2x -it won't let me do it as a fraction- using core 1 a level maths?

Answer 1

Let y = 1/(2x). We want to find dy/dx (or y' depending on which notation you prefer).

To use the usual rule of 'bringing the power down and then reducing the power by 1', we will first change 1/x to x-1 (ie x to the power of -1).

y = x-1/2

dy/dx = -x-2/2 (bringing down the power of -1, and then reducing the power by 1 to get -2)

We can then remove the negative power of x by sending it to the bottom of the fraction.

dy/dx = -1/(2x-2)

Sorry to intrude dude, but you left the negative power in when sending it to the bottom, the answer should be -

dy/dx = -1/(2x2)