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यदि ` y= sin ^(-1) {(5x+ 12sqrt (1-x^(2)))/(13)}` तब `(dy)/(dx)` का मान ज्ञात कीजिए|

Answer» `" "y= sin ^(-1) {(5x+12sqrt(1-x^(2)))/(13)}`
` rArr y=sin ^(-1) {(5x)/(13)+ (12)/(13) sqrt(1-x^(2))}`
माना ` (5)/(13)=sin alpha ` तथा ` x =cos theta ,` तब
` cos alpha =sqrt(1-(25)/(169))= sqrt((144)/(169))=(12)/(13)`
व् ` sqrt(1-x^(2))=sqrt (1-cos ^(2))theta =sqrt (sin ^(2) theta =sin theta )`
` y=sin ^(-1) {sin alpha cos theta +cos alpha sin theta }`
` =sin ^(-1) {sin (alpha +theta ) } `
` " "y= (alpha +theta )= sin ^(-1) ""(5)/(13) +cos ^(-1) x `
` therefore " "(dy)/(dx) =(d)/(dx) {sin ^(-1) ""(5)/(13) +cos ^(-1) x}`
` =(d)/(dx) {sin ^(-1)"" (5)/(3)} +(d)/(dx)(cos ^(-1) x)`
` =0 -(1)/(sqrt(1-x^(2)))=-(1)/(sqrt(1-x^(2)))`


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