InterviewSolution
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InterviewSolution
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फलन `tan x^(2)` का प्रथम सिद्धांत से अवलंकन गुणांक ज्ञात कीजिएः |
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Answer» `y=tan x^(2)` ........(i) `therefore y=deltay=tan (x+deltax)^(2)` ........(ii) `therefore y+deltay-y=tan(x+deltax)^2-tanx^(2)` `=(sin (x+deltax)^(2))/(cos(x+deltax)^(2))-(sin x^(2))/(cos x^(2))` `=(sin(x+deltax)^(2)cosx^(2)-cos(x+deltax)^(2)sinx^(2))/(cos (x+deltax)^(2).cosx^2)` `=sin [(x+deltax)^(2)-x^(2)]/(cos (x+deltax)^2cosx^(2))` `=(sin(x^2+deltax^(2)+2xdeltax-x^(2)))/(cos((x+deltax)^(2)cos))` दोनों पक्षों को `deltax` से भाग देकर `underset(deltax to 0)lim` लेने पर `underset(deltax to 0)lim (deltay)/(deltax)=(dy)/(dx)` `underset(deltax to 0)lim (sin deltax(2x+deltax))/(deltax(2x+deltax)).underset(deltax to 0)lim (2x+deltax)/(cos (x+deltax)^(2).cosx^(2))` `=1.underset(deltax to 0)lim (2x+deltax)/(cos (x+deltax)^(2).cosx^(2))` `=(2x+0)/(cos (x+0)^(2) cos x^(2))xx1` `=(2x)/(cos^(2)x^(2))=2x sec^(2)x^2` `therefore (d)/(dx)(tan x^(2))=2x sec^(2) x^(2)` |
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