That makes sense thank youphyzguy 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.
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##.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) ?
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.
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.
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.
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.
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.