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I would like to start by saying that I'm not at school, I'm 40 years old, and learning calculus for the first time - personal, private study - so anyone helping me out won't be giving me the answers to any course work or school work. I don't have a teacher, and there's no one I can ask who can help me, so I've come to this forum hoping some kind soul can help me.

I'm trying to understand how to differentiate y=x^n, but I get stuck at the expansion stage

In all cases, we are increasing y by a small amount (dy)

Example 1:

y+dy = (x+dx)^2

expanded out, it becomes: y+dy = x^2 + 2x.dx+(dx)2

Example 2:

y+dy = (x+dx)^3

expanded out, it becomes y+dy = x^3 + 3x^2.dx+3x(dx)^2+(dx)^3

Final Example:

y+dy = (x+dx)^4

expanded out, it becomes y+dy = x^4 + 4x^3dx+6x^2(dx)^2 + 4x(dx)^3 + (dx)^4

My calculus textbook assumes a knowledge I don't have.

Can someone please explain clearly & simply how one is supposed to derive these expanded expressions? Or even refer me to an external link which explains it?

Many thanks

## Homework Statement

I'm trying to understand how to differentiate y=x^n, but I get stuck at the expansion stage

## Homework Equations

In all cases, we are increasing y by a small amount (dy)

Example 1:

y+dy = (x+dx)^2

expanded out, it becomes: y+dy = x^2 + 2x.dx+(dx)2

Example 2:

y+dy = (x+dx)^3

expanded out, it becomes y+dy = x^3 + 3x^2.dx+3x(dx)^2+(dx)^3

Final Example:

y+dy = (x+dx)^4

expanded out, it becomes y+dy = x^4 + 4x^3dx+6x^2(dx)^2 + 4x(dx)^3 + (dx)^4

My calculus textbook assumes a knowledge I don't have.

Can someone please explain clearly & simply how one is supposed to derive these expanded expressions? Or even refer me to an external link which explains it?

Many thanks

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