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Question
Find the derivative of f(x) = x3, by first principle.
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Solution
By definition,
f'(x) = `lim_(h -> 0) (f(x + h) - f(x))/h`
= `lim_(h -> 0) ((x + h)^3 - x^3)/h`
= `lim_(h -> 0) (x^3 + h^3 + 3xh(x + h) - x^3)/h`
= `lim_(h -> 0) (h^2 + 3x(x + h))`
= `3x^2`
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