Derivative function (and sum of cube ) confusion

[dkeller1]

just curious why when finding derivative function of f(x) = x^3 - 12x

for (x + deltaX)^3 we use the method (x + deltaX)(x + deltaX)(x + deltaX) rather than sum of cubes (x + deltaX)(x^2 - xdeltaX + deltaX^2) ?

here is a snippet of a problem ..

.

what am I missing ?

 

[Deleted member 4993]

just curious why when finding derivative function of f(x) = x^3 - 12x

for (x + deltaX)^3 we use the method (x + deltaX)(x + deltaX)(x + deltaX) rather than sum of cubes (x + deltaX)(x^2 - xdeltaX + deltaX^2) ?

here is a snippet of a problem ..

.

what am I missing ?

Look at the identities below:

a³ + b³ = (a + b)(a² - ab + b²)...........................(1)

and

(a + b)³ = a³ + 3a²b + 3ab² + b³ .............................(2)

Your function looks like (2).You see, for example,:
a³ + b³ = 2³ + 3³ = 35

and

(a + b)³ = (2 + 3)³ = 125

Those are not same!!!

 

[dkeller1]

Look at the identities below:

a³ + b³ = (a + b)(a² - ab + b²)...........................(1)

and

(a + b)³ = a³ + 3a²b + 3ab² + b³ .............................(2)

Your function looks like (2).You see, for example,:
a³ + b³ = 2³ + 3³ = 35

and

(a + b)³ = (2 + 3)³ = 125

Those are not same!!!

Ok I see then.

I was seeing (a + b)³ as being the same as a³ + b³

and reverse being able to happen such as the 3 being able to be pulled out of a³ + b³ to = (a + b)³ ..
My mind was telling me when you distribute powers you simply multiply the 3 time the a^1 to get a^3 + b^3 which equaled the same thing



little confusion