## anonymous one year ago I have no idea how to solve this. Can someone please help me for a medal? :) (posting below)

1. anonymous

$\frac{ f(x+Δx)−f(x) }{ Δx }$ if f(x) = x^2

2. IrishBoy123

compute as $$\huge \frac{(x + \Delta x)^2 - x^2}{\Delta x}$$

3. IrishBoy123

so expand out the $$\large (x + \Delta x)^2$$ in the numerator :p

4. anonymous

I know how to get to the expanding part, but I am not sure how to expand the numerator. Could you show me how?

5. anonymous

Would it end up looking like this... $\frac{ x^{2} + Δx^{2}-x^{2} }{ Δx }$

6. IrishBoy123

first expand out $$(x+Δx)^2$$ on its own that's $$(x+Δx) \times (x+Δx)$$

7. IrishBoy123

|dw:1440705634106:dw|

8. anonymous

That makes sense, but how do you multiple an "Δx" by an "x"

9. IrishBoy123

$$x \times \Delta x = x \ \Delta x$$

10. anonymous

So the numerator would end up being... $\frac{ x^{2}+2xΔx+Δx^{2}-x^{2} }{ Δx }$ which would simplify to... $\frac{ 2xΔx+Δx^{2} }{ Δx }$ is that correct?

11. IrishBoy123

$\checkmark$

12. IrishBoy123

now finish it!

13. anonymous

$\frac{ Δx(2x+Δx) }{ Δx }$ And the final answer would be... 2x+Δx ?

14. IrishBoy123

yay! well done learning calculus? happy days!

15. anonymous

Thank you so much. :)

16. IrishBoy123

any time! thank you.

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