Differentiating

[stopandthink]

[math] y= x^3[/math]

 

[math] y+dy= (x+dx)^3 [/math]

 

My question is how would i go about cubing x+dx? I can use the foil method easily with squaring, but i can't quite see how on this.

[Greg H.]

You have to FOIL twice, basically.

 

So you do (x+dx) * (x+dx) then multiply the product by (x+dx) again.

 

My question is why are you bothering to do all this work when a simple application of the product rule will get the result you need.

[stopandthink]

Like this?

 

[math] x^2+dx(x)+dx(x)+dx^2(x+dx) [/math]

 

 

---I have absolutely no clue as to what to do next

Edited October 19, 2012 by stopandthink

[Greg H.]

Like this?

 

[math] x^2+dx(x)+d(x)+dx^2(x+dx) [/math]

 

Yeah, though I would write it like this to avoid confusion

 

[math] (x^2+2dx(x)+dx^2)\times(x+dx) [/math]

[stopandthink]

Yeah, though I would write it like this to avoid confusion

 

[math] (x^2+2dx(x)+dx^2)\times(x+dx) [/math]

 

Could you explain how to use the foil method on this?

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I'm just going to review the binomial theorem.

Edited October 19, 2012 by stopandthink

[Greg H.]

Could you explain how to use the foil method on this?

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I'm just going to review the binomial theorem.

 

It's not really FOIL at this point. It's just brute force multiplication.