# Derivatives: Solving a Substitution Error on MathsIsFun

• B
• kolleamm
This is just a different way of writing the same equation.In summary, the process of finding the derivative involves taking the input value of a function, adding a small change (dx or Δx), and then squaring the result. This is represented as f(x+dx) = (x+dx)^2. It may seem like it should be (x^2 + dx^2), but this is incorrect because the function f(x) = x^2 squares its input value, not the sum of its input value and a small change.
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

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
phyzguy said:
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

kolleamm said:
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##.

## 1. What is a substitution error in derivatives?

A substitution error in derivatives occurs when a wrong value is substituted for a variable in a derivative equation. This can lead to incorrect results and can be a common mistake when solving derivatives.

## 2. How do I identify and fix a substitution error in derivatives?

To identify a substitution error, carefully check each step of your derivative calculation and make sure the correct values are substituted for each variable. If an error is found, simply correct the substitution and continue with the calculation.

## 3. Can a substitution error change the outcome of a derivative calculation?

Yes, a substitution error can significantly change the outcome of a derivative calculation. This is because a small change in a variable can lead to a large change in the final result of a derivative equation.

## 4. Are there any common types of substitution errors in derivatives?

Yes, there are a few common types of substitution errors in derivatives. These include using the wrong value for a variable, missing a negative sign, and using incorrect algebraic rules when simplifying the equation.

## 5. How can I avoid making substitution errors in derivatives?

To avoid making substitution errors in derivatives, it is important to carefully double-check each step of your calculation and make sure the correct values are substituted for each variable. Additionally, practicing and familiarizing yourself with common algebraic rules can also help reduce the likelihood of making substitution errors.

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