If y = 1/x^3, find an expression for dy/dx
Write down y = 1/x3 This can be rewritten as y = 1x-3 or just y = x-3 as if the x is on the bottom of the fraction, it can be rewritten with a negative version of the power 3. A simple way of working this out is if you look at the fraction sign, you can shrink it into a negative sign and slot it on the right of the x and the left of the number (to help visual learners). To clarify this and give another example, if y = 1/x2, that would be re-written as y = 1x-2 (or y = x-2). A third example, if y = 2/x2, it would be re-written as y = 2x-2.Anyway, going back to the question, now we have the y = x-3, we need to do differentiation on it. The way this works is for the first step we bring that -3 down to the left-hand side of the x, making -3x. The second step is we minus 1 from the power of -3, so that makes -4 (as -3 -1 = -4). Then we have to combine the 2 steps. So we have the -3x from the first step and then -4 from the second step. We then join them together like so: -3x-4 and that is our answer.
