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Find the derivative of s in x3 from firs...

Find the derivative of `s in x3` from first principles.

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Verified by Experts

Herte, `f(x) = root3 (sinx)`
`:. f'(x) = Lim_(h->0) (f(x+h) - f(x))/h`
`= Lim_(h->0) (root3(sin(x+h)) - root3(sinx))/h`
As this is a `0/0`form. So, we will apply `L'`hospital rule to evaluate this limit and differentiate it w.r.t. `h`.
`= Lim_(h->0) (1/3(sin(x+h)^(-2/3)(cos(x+h))) - 0)/1`
`= 1/3 (sinx)^(-2/3)cosx`
`:. f'(x) = 1/3 (sinx)^(-2/3)cosx`
`
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