1.

`x^(2)log x ` का द्वितीय अवकलज ज्ञात कीजिए|

Answer» माना ` " " y= x ^(2) logx`
` therefore " "(dy)/(dx) =x^(2) (d)/(dx) log x + log x (d)/(dx) x^(2)`
` " "= x +2x log x `
` rArr " "(dy)/(dx) =x (1+ 2log x ) `
पुनः x के सापेक्ष अवकलज करने पर
` (d)/(dx) ((dy)/(dx))=(d^(2)y)/(dx^(2))`
` " "=x (d)/(dx) (1+2log x )+ (1+2log x ) (d)/(dx)x `
` " "= x [0+2*(1)/(2)] + (1+2log x ) `
` " "= 2+1 +2log x `
` therefore " "(d^(2)y)/(dx^(2))=(3+2log x )`


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