निम्न फलनों का x के सापेक्ष अवकल गुणांक ज्ञात कीजिए|
` (i)" "(1)/((x+p)(x+q)(x+r)) `
`(ii)" "((x-sin x )^(3//2))/(sqrt(x))`

Explanation

(i )माना ` " "y= (1)/((x+p)(x+q)(x+r))`
` rArr log y=log [(1)/((x+p)(x+q)(x+r))]`
` " "` (दोनों ओर का लघुगणक लेने पर)
` " "= log 1- log (x+p)-log (x+q) -log (x+r)`
x के सापेक्ष दोनों पक्षों का अवकलन करने पर
` (1)/(y) (dy)/(dx) =0-(1)/(x+p)-(1)/(x+q) -(1)/(x+r)`
` rArr (dy)/(dx) =-y[(1)/(x+p) +(1)/(x+q)+(1)/(x+r) ]`
` " "=- (1)/((x+p)(x+q)(x+r) )[(1)/(x+p)+ (1)/(x+q)+(1)/(x+r)]`
`(ii) y= (x-sin x )^(3//2)/(sqrt(x))`
` rArr " "log y= log [ ((x-sin x )^(3//2))/sqrt(x)]`
` " "=(3)/(2) log (x-sin x ) -(1)/(2)log x `
दोनों पक्षों का x के सापेक्ष अवकलन करने पर
` " "(1)/(y)(dy)/(dx) =(3)/(2) *(1)/(x-sin x )(1-cos x ) -(1)/(2)*(1)/(x)`
`rArr " "(dy)/(dx) = y [(3)/(2)*(1-cos x )/((x-sin x ) )- (1)/(2x )]`
` rArr" "(dy)/(dx) =((x - sin x)^(3//2))/(2sqrt(x))[(3(1-cos x ))/(x-sin x ) -(1)/(x)]`