यदि ` y = tan^(-1). (3a^(2)x-x^(3))/(a (a^(2) - 3x^(2)) )` तो `(dy)/(dx)` का मान ज्ञात कीजिए ।

Explanation

` y = tan ^(-1) ( 3a^(2)x - x^(3))/(a( a^(2) - 3x^(2) ))`
` :. y = tan^(-1) [ (3a^(2) [ a tan theta] - [ a tan theta ]^(3) )/ ( a {a^(2) - 3 ( a tan theta )^(2) })]`
` tan^(-1) [( 3a^(3) tan theta - a^(3) tan^(3) theta )/(a^(3) [ 1- 3 tan ^(2) theta])]`
` tan^(-1) [(3 tan theta - tan ^(3) theta) /(1- 3 tan^(2) theta)] `
` tan^(-1) [ tan 3 theta ] = 3 theta = 3 tan^(-1) [ x//a] `
x के साक्षेप अवकलन करने पर
` dy/dx = 3 d/ dx [ tan ^(-1) ( x // a )]`
` = 3 . 1/(1+ (x//a)^(2) )d/dx [x/a] `
` ( 3a^(2))/ ( a^(2) + x^(2))*1/2 = (3a)/(a^(2) + x^(2))`