x के साक्षेप ` sqrt(( x-3)(x^(2) + 4))/(3x^(2) + 4x + 5 ) ` का अवकलन कीजिए ।

Explanation

माना ` y = sqrt(((x-3) (x^(2) + 4) )/ ( 3x^(2) + 4x + 5 ) )`
दोनों पक्षों में log लेने पर ,
` log y = 1/2 [log ( x- 3) + log (x^(2) + 4) - log (3x^(2) + 4x +5) ]`
` 1/y . dy/dx = 1/2 [1/(x-3) + (2x)/(x^(2) +4) - (6x + 4) / ( 3x^(2) + 4x +5)]`
` 1/y . dy/dx = 1/2 [1/(x-3) + (2x)/(x^(2) +4) - (6x + 4) / ( 3x^(2) + 4x +5) xx ( 6x+4)]`
` dy / dx = y/2 [ 1/(x-3) + (2x)/(x^(2) + 4) - ( 6x + 4) /( 3x^(2) + 4x + 5) ]`
` = 1/2 sqrt(((x - 3 ) ( x^(2) +4))/( 3x^(2) + 4x + 5 ))[ 1/(x-3) + (2x)/( x^(2) +4) - ( 6x + 4)/( 3x^(2) + 4x + 5 )]`