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यदि ` y= tan ^(-1) ((x^(1//3)+a^(1//3))/(1-x^(1//3)a^(1//3)))` तब ` (dy)/(dx) ` का मान ज्ञात कीजिए|

Answer» `y= tan ^(-1) ((x^(1//3)+a^(1//3))/( a-x^(1//3)a^(1//3)))`
माना `x^(1//3) =tan theta ` तथा ` a^(1//3) =tan phi ,` तब
`y=tan ^(-1) ((tan theta + tanphi )/(1-tan theta tan phi ))= tan ^(-1) [tan (theta +phi ]`
` y= theta +phi=tan ^(-1)(x^(1//3) )+tan ^(-1) (a^(1//3))`
` therefore " "(dy)/(dx) =(d)/(dx) {tan ^(-1) (x^(1//3)) +tan ^(-1) (a^(1//3))}`
` " "= (d)/(dx) {tan ^(-1) (x^(1//3))} +(d)/(dx) {tan ^(-1) (a^(1//3))}`
` =(1)/(1+x^(2//3) )*(1)/(3)x ^(-2//3) +0 =(1)/(3x^(2//3)(1+x^(2//3)))`


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