0
$\begingroup$

I'm trying to brush up on my algebra and differentiation, I'm self-learning so I don't have a way to figure out this simple mistake I've made other than asking here, so sorry if this is a bit noob -

All my working out for calculating the derivative of $1/x$ using the general gradient function is below, the answer given in my textbook is circled at the bottom. As you can see I've got too many $\delta x$s in my denominator in my answer, but I can't figure out where I've gone wrong. I have a feeling it must be step 1 -> 2 - but why / how?

My textbook uses a slightly different approach to solve it, working out $f(x - \delta x) - f(x)$ first, simplifying that on it's own, THEN dividing by $\delta x$ - I guess that's a simpler (better?) approach but it means I can't follow through my workings with the textbook workings.

Thanks!

enter image description here

$\endgroup$

1 Answer 1

Reset to default
0
$\begingroup$

The mistake happens in the last line.

$$\frac{-\delta x ^2}{x^2\cdot\delta x^2 - x\cdot\delta x^3}\neq \frac{-1}{x^2\cdot\delta x + x\cdot\delta x ^2}$$

You need to factor $\delta x$ out in the numerator to get

$$x^2\cdot\delta x^2 - x\cdot\delta x^3 =\delta x^2 (x^2-x\cdot\delta x)$$

$\endgroup$
1
  • $\begingroup$ {slaps head} d'oh! Thanks, that's so embarrasingly obvious now $\endgroup$ Commented Sep 17, 2015 at 17:23

You must log in to answer this question.

Start asking to get answers

Find the answer to your question by asking.

Ask question

Explore related questions

See similar questions with these tags.