- #1
christian0710
- 409
- 9
Hi, my Calculus book (Elementary Calculus an Infinitesimal approach) uses a mathematical argument, and I'm not sure if it's correct so i thought i wuold check with you guys :)
When the book want's to find the derivative of f(x)=x^2 the books starts like this
y=x2
Δy +y = (x + Δx)2
So my question is this: Is it mathematically correct to write
Δy+y = (x + Δx)2.
To me it looks more like the left side should translate into a right side that looks like this
Δy+y = x2 + (Δx)2
I'm asuming that Δy+y translates into f(Δx+x) and not f(x)+f(Δx) but to me it looks as if Δy+y is f(x)+f(Δx) which is not the same as f(Δx+x)
If the above is true, does that mean that this is also true?
if y=x2 then.
y=x2
y+1/y = (x+1/x)2 and would this be the same as f(x+1/x)?
When the book want's to find the derivative of f(x)=x^2 the books starts like this
y=x2
Δy +y = (x + Δx)2
So my question is this: Is it mathematically correct to write
Δy+y = (x + Δx)2.
To me it looks more like the left side should translate into a right side that looks like this
Δy+y = x2 + (Δx)2
I'm asuming that Δy+y translates into f(Δx+x) and not f(x)+f(Δx) but to me it looks as if Δy+y is f(x)+f(Δx) which is not the same as f(Δx+x)
If the above is true, does that mean that this is also true?
if y=x2 then.
y=x2
y+1/y = (x+1/x)2 and would this be the same as f(x+1/x)?
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