- #1

christian0710

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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=x

Δy +y = (x + Δx)

So my question is this: Is it mathematically correct to write

Δy+y = (x + Δx)

To me it looks more like the left side should translate into a right side that looks like this

Δy+y = x

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=x

y=x

y+1/y = (x+1/x)

When the book want's to find the derivative of f(x)=x^2 the books starts like this

y=x

^{2}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 = x

^{2}+ (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=x

^{2}then.y=x

^{2}y+1/y = (x+1/x)

^{2 }and would this be the same as f(x+1/x)?
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