Find the derivative of `sqrt(tanx)` using first principles. – InterviewSolution

InterviewSolution

1.	Find the derivative of `sqrt(tanx)` using first principles.
Answer» `f(x) = sqrt(tanx)` `Lim_(h->0) (f(x+h)-f(x))/h = Lim_(h->0) (sqrt(tan(x+h))-sqrt(tanx))/h` Multiplying nunerator and denominator by `(sqrt(tan(x+h))+sqrt(tanx))`, ` =Lim_(h->0) (tan(x+h) - (tanx))/ ((sqrt(tan(x+h))+sqrt(tanx))h)` `=Lim_(h->0) ((sin h)/(cos(x+h)cosx))/ ((sqrt(tan(x+h))+sqrt(tanx))h)` `= Lim_(h->0) sin h/h xx Lim_(h->0)(1/((cos(x+h)cosx)(sqrt(tan(x+h))+sqrt(tanx))))` `=1 xx 1/(2cos^2xsqrt(tanx))` `=sec^2x/(2sqrttan x)`

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