यदि `y=tan^(-1){(3a^(2)x-x^(3))/(a(a^(2)-3x^(2)))}`, तो `((dy)/(dx))` का मान ज्ञात कीजिये ।

Explanation

`y=tan^(-1){(3a^(2)x-x^(3))/(a(a^(2)-3x^(2)))}`
`x=atan theta ` रखने पर ,
`y=tan^(-1){(3a^(2)a tan theta - a^(3) tan ^(3) theta)/(a (a^(2)-3a^(2)tan^(2)theta))}`
या `y=tan^(-1){(3tan theta - tan^(3) theta)/(1-3 tan^(2)theta)}`
या `y = tan^(-1) (tan 3 theta) या y =3theta`
या `y=3 tan^(-1)((x)/(a))`
या `(dy)/(dx)=3(1)/(1+(x^(2))/(a^(2)))(1)/(a)=(3a)/(a^(2)+x^(2))`