1.

यदि `y= tan ^(-1) ((a)/(x))+log sqrt((x-a)/(x+a))` तब सिद्ध कीजिए की ` (dy)/(dx) =(2a^(3) )/(x^(4)-a^(4))`

Answer» `y=tan ^(-1) ((a)/(x) )+ log sqrt((x-a)/(x+a))`
` = tan ^(-1) ""(a)/(x)+(1)/(2) [log (x-a )-log (x+a ) ]`
` rArr " "(dy)/(dx) =(1)/(1+(a^(2))/(x^(2)))*(d)/(dx) ((a)/(x) )+ (1)/(2) [((x+a) -(x-a))/(x^(2)-a^(2))]`
` " "=(x^(2) )/(x^(2) +a^(2))*a(-(1)/(x^(2))) +(1)/(2) [((x+a)-(x-a))/(x^(2)-a^(2))]`
` " "= (-a) /(x^(2)+a^(2))+(a) /(x^(2)-a^(2))`
` =(-a(x^(2)-a^(2))+a(x^(2)+a^(2)))/(x^(4)-a^(4)) =(2a^(3))/(x^(4)a^(4))`


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