1.

`e^(tan ^(-1))sqrt (x) ` के लिए `(dy)/(dx)` का मान ज्ञात कीजिए|

Answer» `y=e ^(tan ^(-1)sqrt (x))`
माना ` sqrt x=t , tan ^(-1) sqrt (x) =tan ^(-1)t=u`
` therefore " "y= e^(u) `
` rArr (dy)/(du) =e^(u) ,(du)/(dt) =(1)/((1+ t^(2) ) ),(dt)/(dx) =(1)/(2) xx^(-1//2) =(1)/(2sqrt x)`
हम जानते है की
` (dy)/(dx) =((dy)/(du) xx(du)/(dt)xx(dt)/(dx))=e^(u) (1)/((1+t^(2) ) )*(1)/(2sqrt (x) ) `
` =e ^(tan ^(-1) t)*(1)/((1+t^(2) ))*(1)/(2sqrt (x) )` जहाँ `u= tan ^(-1) t `
` =(e^(tan -1 sqrtx ) )/(2sqrt x(1+x) ) , " "` जहाँ ` t= sqrt x`
` (dy)/(dx) =(e^(tan -1sqrt x))/(2sqrt x (1+x))`


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