निम्न फलन का x के सापेक्ष अवकलन कीजिये|
` (i) x^(x) +(sin x )^(sin x)`

Explanation

माना ` " "y= x^(x) +(sin x )^(sin x )`
माना ` " " y_1 =x^(x) ` तथा ` y_2 =(sin x)^(sin x ) `
` therefore " " y=y_1 +y_2 " "...(1)`
punha ` " "y_1 =x^(x) `
` therefore " "(dy_1)/(dx) =x^(x) [1+log x ] ` [udahran (1 )(i ) से ] तथा ` " "y_2 =(sin x)^(sin x ) `
दोनों पक्षों का लघुगणक लेने पर,
` log y_2 =sin x log sin x `
दोनों पक्षों का x के सापेक्ष अवकलन करने पर,
` (d)/(dy_2) log y_2""(dy_2)/(dx) =sin x(d)/(dx) log sin x+ log sin x (d)/(dx) sin x `
` rArr " "(1)/(y_2) (dy_2) /(dx) =cos x+ cos x log sin x `
` " " =cos x (1+log sin x ) `
` rArr " "(dy_2)/(dx) =y_2 cosx (1+log sin ) `
` " "= cos x (sinx ) ^(sin x) [ 1+ log sin x ] " "...(3)`
समी० (1 ) ,(2 ) व् (3 ) से,
` (dy)/(dx) =x^(3) (1+log x ) + cos x (sin x ) ^(sinx) [1+ log sin x ]`