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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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