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प्रश्न
Find the derivative of the following function from first principle.
x3 – 27
उत्तर
Let f(x) = x3 – 27. Accordingly, from the first principle,
`f'(x) = lim_(h->0)(f(x + h) - f(x))/h`
= `lim_(h->0)([(x + h)^3 - 27] - (x^3 - 27))/h`
= `lim_(h->0)(x^3 + h^3 + 3x^2h + 3xh^2 - x^3)/h`
= `lim_(h->0) (h^3 + 3x^2h + 3xh^2)/h`
= `lim_(h->0) (h^3 + 3x^2 + 3xh)`
= 0 + 3x2 + 0
= 3x2
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