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The Derivative of a Constant

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Lesson Parent:

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.

Solution:

Recall that

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

In this particular problem we have

Now the derivative is

But we know that

and therefore