AP EAMCET201823 Apr 2018Morning ShiftMathematicsDifferentiationActual
If x= - , y= ^n - ^n then d y d x =
Options
- Ay^2+4 x^2+4
- Bn y^2+4 x^2+4
- Cx^2+4 y^2+4
- Dn x^2+4 y^2+4
Correct answer
B. n y^2+4 x^2+4
Step-by-step solution
(b) We have, x= - differential w.r.t aligned d x d & = + & = + & = ( + ) aligned Now, y= ^n - ^n differential w.r.t ' ' aligned d y d & =n ^ n-1 -n ^ n-1 (- ) & =n ^n +n ^ n-1 & =n ( ^n + ^n ) & =n ( ^n + ^n ) aligned Now, aligned & d y d x = n ( ^n + ^n ) ( + ) & d y d x = n ( ^n + ^n ) ( + ) aligned Squaring both side aligned & ( d y d x )^2= n^2 ( ^n + ^n )^2 ( + )^2 & ( d y d x )^2= n^2 ( ^ 2 n + ^ 2 n +2 ) ( ^2 + ^2 +2 ) & = n^2 ( ^ 2 n + ^ 2 n -2+4 ) ( ^2 + ^2 -2+4 ) & = n^2 [ ( ^n - ^n )^2+4 ] ( - )^2+4 & (