InterviewSolution
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InterviewSolution
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निम्नलिखित फलनों का x के सापेक्ष अवकलन कीजिए- `sin(2sin^(-1)x)` |
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Answer» `y=sin(2sin^(-1)x)` माना `x=sintheta`, तब `theta=sin^(-1)x` `thereforey=sin2theta` `rArry=2sinthetacostheta` `rArry=2xsqrt(1-x^(2))`, `[becausecostheta=sqrt(1-sin^(2)theta)=sqrt(1-x^(2))]` दोनों पक्षों का x के सापेक्ष अवकलन करने पर, `(dy)/(dx)=2d/(dx){x(sqrt(1-x^(2)))}` `rArr(dy)/(dx)=2[xd/(dx)(sqrt(1-x^(2)))+(sqrt(1-x^(2)))d/(dx)(x)]` `rArr(dy)/(dx)=2[x.1/2(1-x^(2))^(-1//2)d/(dx)(1-x^(2))+sqrt(1-x^(2)).1]` `rArr(dy)/(dx)=2[x/(2sqrt(1-x^(2)))xx(-2x)+sqrt(1-x^(2))]` `rArr(dy)/(dx)=2[(-x^(2))/(sqrt(1-x^(2)))+sqrt(1-x^(2))]` `(dy)/(dx)=2[(-x^(2)+(1-x^(2)))/(sqrt(1-x^(2)))]` `=(2(1-2x^(2)))/(sqrt(1-x^(2)))` |
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