1.

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

Answer» माना ` " "y= e^(sin x ^(2))`
` rArr " "(dy)/(dx) =e^(sin x ^(2))*cos x^(2) *2x`
` rArr " "(dy)/(dx) =2xcos x^(2) e^(sin x^(2))=2xcos x^(2)y`
` " " (becausey= e^(sin x ^(2)))`
पुनः x के सापेक्ष अवकलन करने पर
`(d)/(dx) ((du)/(dx) )= 2 [(xcos x^(2))(dy)/(dx)+ y{cos x ^(2) -2x^(2) sin x ^(2)}]`
` = 2[ 2 x^(2) cos ^(2) x^(2) e^(sin x ) +e^(sin x ^(2))(cos x^(2) -2x ^(2)sin x^(2))]`
` =2e^(sin x ^(2) )[2x ^(2)cos ^(2)x^(2)+ cos x^(2) -2x^(2) sin x ^(2) ]`


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