The Power Rule.
Power Rule is one of the Techniques of Differentiation.
The Power Rule states that:
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:
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:
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