InterviewSolution
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InterviewSolution
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x के सापेक्ष अवलन कीजिये - `e^(sec^(2))+"3 cos x"^(-1)x+x^(x)` |
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Answer» `y=e^(sec^(2)x)+3 cos ^(-1)x + x^(x)` `rArr (dy)/(dx) = e^(sec^(2)x)(d)/(dx)(sec^(2)x)+3(-(1)/(sqrt(1-x^(2))))+(d)/(dx)(x^(x))` `rArr (dy)/(dx) = e^(sec^(2)x)2secx (d)/(dx)(sec x)- (3)/(sqrt(1-x^(2)))+ x^(x)(1+log x)` `{:(,|,y=x^(2),),(,rArrlog y = x log x ,,),(,rArr(1)/(y)(dy)/(dx)=x.(1)/(x)+1.log x ,,),(,rArr(1)/(y)(dy)/(dx)=(1+log x),,),(,rArr (dy)/(dx)=y(1+log x),,),(,rArr(dy)/(dx)=x^(2)(1+log x),,):}` `=e^(sec^(2)x).2sec x . sec x tan x -(3)/(sqrt(1-x^(2)))+x^(2)(1+logx)` `2 sec^(2) x tan x e^(sec^(2)x)-(3)/(sqrt(1-x^(2)))+x^(x)(1+logx)` |
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