The Derivative of a Constant

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

Show that
\[
\frac{df}{dx}=0
\]
when $f(x)$ is a constant.

Answer: 

It is true that the derivative of a constant is zero.

SAMPLE SOLUTION

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Solution: 

Recall that

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Since $f(x)$ is a constant let's denote it by <Sign in to see all the formulas>. Now let's construct the function

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In this particular problem we have

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Now the derivative is

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But we know that

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and therefore

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