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Question

Find the derivative of f(x)=x2.

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Solution

Given : f(x)=x2
We know that f(x)=limh0f(x+h)f(x)h
f(x)=limh0(x+h)2x2h
f(x)=limh0x2+h2+2xhx2h
f′′(x)=limh0h2+2xhx2+x2h
f(x)=limh0h(h+2x)+0h
f(x)=limh0h(h+2x)h
f(x)=limh0(h+2x)
f(x)=0+2x
f(x)=2x
Hence, f(x)=2x

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