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Use theh0definition of the derivative to prove the power rule holds for positive integers powers

Short Answer

Expert verified

We prove the power rule holds for positive integers powers using the definition of derivative

Step by step solution

01

Given information

We are given a function asf(x)=xn, Where n is a positive integer

02

Find the derivative

We use definition of the derivative

We have,

limh0f(x+h)-f(x)hlimh0(x+h)n-xnhlimh0xn+nxn-1h+.....+hn-xnh[binomialexpansion]limh0nxn-1h+.....+hnhlimh0h(nxn-1+....+hn-1)hlimh0(nxn-1+....+hn-1)=nxn-1

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