# Thread: need help with algebra finding derivative

1. ## need help with algebra finding derivative

Show that the slope of y = x^3 - 3x + 3 at any x is 3x^2 - 3

A=delta (dont know how to do delta)

im doing it using this method
( (x+Ax)^3 - 3(x+Ax) + 3 ) - ( x^3 - 3x + 3 ) / ( (x+Ax) - x )

i simplify and get Ax^2 + 3xAx + 3x^2 - 6x

2. Originally Posted by stones44
Show that the slope of y = x^3 - 3x + 3 at any x is 3x^2 - 3

A=delta (dont know how to do delta)

im doing it using this method
( (x+Ax)^3 - 3(x+Ax) + 3 ) - ( x^3 - 3x + 3 ) / ( (x+Ax) - x )

i simplify and get Ax^2 + 3xAx + 3x^2 - 6x
where did 6x come from?

you simplified something wrong. expanding everything, you should get:

$\lim_{\Delta x \to 0} \frac {x^3 + 3x^2(\Delta x) + 3x(\Delta x)^2 + (\Delta x)^3 - 3x - 3 \Delta x + 3 - x^3 + 3x - 3}{\Delta x}$

now cancel what is to be canceled, simplify as much as possible, and take the limit

3. Originally Posted by Jhevon
where did 6x come from?

you simplified something wrong. expanding everything, you should get:

$\lim_{\Delta x \to 0} \frac {x^3 + 3x^2(\Delta x) + 3x(\Delta x)^2 + (\Delta x)^3 - 3x - 3 \Delta x + 3 - x^3 + 3x - 3}{\Delta x}$

now cancel what is to be canceled, simplify as much as possible, and take the limit
doesnt -3(x+Ax) = -3x + -3Ax ? and then the other -3x so -6x

4. let $h = \Delta x$

$f(x) = x^3 - 3x + 3$

$f(x+h) = (x+h)^3 - 3(x+h) + 3$

$\lim_{h \to 0} \frac{(x+h)^3 - 3(x+h) + 3 - (x^3 - 3x + 3)}{h}$

$\lim_{h \to 0} \frac{x^3 + 3x^2h + 3xh^2 + h^3 - 3x - 3h + 3 - (x^3 - 3x + 3)}{h}$

now, clean it up and finish finding the limit which will give you the derivative of f.

5. i figured what i did wrong

ok so i cleaned it up i have

3x^2 + 3xAx + Ax^2 - 3

shouldnt i end up with (3x^2 - 3) +Ax ?

6. Originally Posted by stones44
doesnt -3(x+Ax) = -3x + -3Ax ? and then the other -3x so -6x
what other -3x? the only other 3x is +3x

7. yeah i see what i did

but i still dont have the answer do i? look at my post above yours

8. Originally Posted by stones44
yeah i see what i did

but i still dont have the answer do i? look at my post above yours
nope, you should end up with $3x^2 + 3x (\Delta x) + (\Delta x)^2 - 3$

and if we let $\Delta x \to 0$ ...?