Derivatives: Solving a Substitution Error on MathsIsFun

[kolleamm]

I'm learning about derivatives and on the website they put the value

x^2 into f(x + dx) and it became
(x + dx)^2

Shouldn't it be (x^2 + dx^2) ?

It's the last example

https://www.mathsisfun.com/calculus/derivatives-dy-dx.html

Thanks in advance!

 

[phyzguy]

You're thinking of it wrong. The function f(x) = x^2 says, "take the input value and square it". So f(x+dx) means "take (x+dx) and square it", which is (x+dx)^2.

 

[kolleamm]

You're thinking of it wrong. The function f(x) = x^2 says, "take the input value and square it". So f(x+dx) means "take (x+dx) and square it", which is (x+dx)^2.

That makes sense thank you

 

[Mark44]

I'm learning about derivatives and on the website they put the value

x^2 into f(x + dx) and it became
(x + dx)^2

Shouldn't it be (x^2 + dx^2) ?

They aren't "putting the value x^2 into f(x + dx)" -- they are saying that $f(x) = x^2$ and are then calculating $f(x + dx)$ (or more likely, $f(x + \Delta x)$ ). As phyzguy noted, the given function squares its input value, so $f(x + \Delta x) = (x + \Delta x)^2 \ne x^2 + (\Delta x)^2$.