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`sin x^(2) ` का x के सापेक्ष प्रथम सिद्धांत से अवकल - गुणांक ज्ञात कीजिए । |
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Answer» माना ` f(x) = sin x^(2)` तब `f ( x+h) = sin ( x + h)^(2)` ` d/(dx) sin x^(2) = lim _( h to 0 ) (sin( x+h)^(2)-sin x^(2))/h` ` = lim _( h to 0 ) ((2cos(x+h)^(2)+x^(2))/2.(sin (x+h^(2))-x^(2))/2)/h` ` lim _( h to 0 )((2cos(x+h)^(2)+x^(2))/2.sin(h+2x)/2)/h ` ` lim _(h to 0 ) ((2cos(x+h)^(2)+x^(2))/2.sin . (h (h +2x))/2 xx ((h + 2x))/2)/(h (( h+2x)/2))` ` 2 lim _( h to 0 ) cos ((2x^(2) + 2hx + h^(2))/2)xx lim _(h to 0 ) ((sin. (h(h+2x))/2)/(h( h + 2x)/2))xx1/2 lim _ ( h to 0 ) ( h + 2x) ` ` = 2x cos x^(2) ` |
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