Derivative of f(x)=−x2

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

What is the derivative of −x2?

Answer: 

−2x

SAMPLE SOLUTION

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Solution: 

Recall that the derivative is defined as

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For the function x2 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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