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Question

Find the derivative of sinx at x=0.

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Solution

Let f(x)=sin x
We know that f(x)=limh0f(x+h)f(x)h
f(x)=limh0sin(x+h)sinxh
Putting x=0
f(0)=limh0sin(0+h)sin(0)h
f(0)=limh0sinh0h
f(0)=limh0sinhh
f(0)=1
Hence, derivative of sinx at x=0 is 1.

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