# The Power Rule.

**Power Rule** is one of the Techniques of Differentiation.

The Power Rule states that:

The Derivative of a Function raised to n’th power is the Product of n , the function raised to the power (n-1)’th and derivative of the function raised to first power.

Mathematically we can write:

We can also further synthesize this relation and prove the rule for Derivative of general Polynomial Function. which states:

**Proof Of Power Rule for Natural N’th Power:**

The power rule is valid for any rational “n”(eg: 4/5) power of a function. But we will prove

the power rule for only natural number power “n” here.

If “f” is a function of “x” then,

By product rule:

And,

Similarly we can find derivative of fourth power , fifth power………. and the same result comes which is:

**Use of Power Rule:**

Find the derivative of:

Solution:

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