InterviewSolution
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InterviewSolution
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निम्नलिखित को x के सापेक्ष अवकलित करें । (i) `"tan"^(-1)(4sqrt(x))/(1-4x)` (ii) `"tan"^(-1)(sqrt(x)-x)/(1+x^(3//2))` |
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Answer» माना कि `y="tan"^(-1)(4sqrt(x))/(1-4x)` (i) `"tan"^(-1)(sqrt(x)-x)/(1+x^(3//2))` `=2tan^(-1)(2sqrt(x))[because"tan"^(-1)(2x)/(1-x^(2))=2tan^(-1)x]` `therefore(dy)/(dx)=2(d)/(dx)("tan"^(-1)2sqrt(x))` `=2(d)/(d(2sqrt(x)))(tan^(-1)2sqrt(x))*(d)/(dx)(2sqrt(x))` `=2*(1)/(1+4x)*2*(1)/(2sqrt(x))=(2)/(sqrt(x)(1+4x))` (ii) माना कि `y="tan"^(-1)(sqrt(x)-x)/(1+x^(3//2))` तो, `y="tan"^(-1)(sqrt(x)-x)/(1+sqrt(x)*x)=tan^(-1)sqrt(x)-tan^(-1)x` `therefore(dy)/(dx)=(d)/(dx)(tan^(-1)sqrt(x))-(d)/(dx)(tan^(-1)x)=(d)/(dsqrt(x))(tan^(-1)sqrt(x))*(d)/(dx)sqrt(x)-(1)/(1+x^(2))` `=(1)/(1+x)*(1)/(2sqrt(x))-(1)/(1+x^(2))=(1)/(2sqrt(x)(1+x))-(1)/(1+x^(2))` |
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