InterviewSolution
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InterviewSolution
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निम्न फलनों का x के सापेक्ष अवकल गुणांक ज्ञात कीजिये ` (i) (tan ^(-1) x ) /( x ) ` ` (ii) x sec ^(-1) x ^(3) `` (iii) (sin ^(-1) x )^(m)` |
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Answer» (i ) माना ` y= (tan ^(-1) x ) /( x ) ` ` therefore (dy)/(dx) =( x(d)/(dx) tan ^(-1) x-tan ^(-1) x (d)/(dx) x)/( x^(2) ) ` ` " "( ( x)/( 1+x^(2) )- tan ^(-1) x)/( x^(2) )` या ` (dy)/(dx) =(x -(1+x^(2) )tan ^(-1) x)/( x^(2) (1+x^(2) ) ) ` (ii) माना ` y = sec ^(-1) x^(3) ` ` therefore " "(dy)/(dx) =x (d)/(dx) sec ^(-1) x^(3) + sec^(-1)x^(3) (d)/(dx) x ` ` = x(1xx3x^(2) )/( x^(3) sqrt (x^(6)) -1)+ sec ^(-1) x^(3) ` ` = (3)/(sqrt (x^(6)) -1 ) +sec ^(-1) x^(3)` माना ` y= (sin ^(-1) x)^(m) ` ` therefore " "(dy)/(dx) =(d)/(dx) (sin^(-1) x )^(m) ` ` " "=m(sin ^(-1) x ) ^(m-1) (d)/(dx) sin ^(-1) x ` ` rArr" "(dy)/(dx) =(m (sin ^(-1) x) ^(m-1))/(sqrt(1-x^(2)))` |
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