Suppose we have the power function xn.

The derivative of this function is given by the power rule, which is one of the most useful of the differentiation rules.

We can prove this rule by starting with the definition of the derivative, and then substituting the power function into the limit equation. Next we use the binomial theorem, shown here, and substitute in our values for a and b. To simplify the computations, we substitute h for the a in the binomimal theorem and x for the b.

By expanding the first term in the numerator using the binomial theorem, we reach this equation.

Combining and reducing terms results in an equation in which all but the first term of the limit contain h.

Thus, after taking the limit, we are left with the power rule.

Now, let's look at another power function.

We find that the value of the derivative of this function when x equals 16 is one-fourth.

Let's use the power rule to find the derivative of the given function. Click the "Submit" button after entering your answer in the text box.

What is the value of the derivative of this function when x equals 16? Click the "Submit" button after entering your answer in the text box.

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