Derivative of $x^2$

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Lesson Parent: 
Differentiation II: The Gory Details of Calculating Derivatives
Problem: 

What is the derivative of $x^2$?

Answer: 

$2x$

SAMPLE SOLUTION

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Solution: 

Recall that the derivative is defined as

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For the function $x^2$ we have

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Recall that we know <Sign in to see all the formulas> and <Sign in to see all the formulas>. Because the limit of a function times a constant is the function's limit times the constant and because $2x$ is a constant here (remember $x$ is some number we can fill in later) we know that

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Furthermore, because the limit of the sum of two functions is the sum of their limits, we have

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