AP EAMCET201922 Apr 2019Morning ShiftMathematicsDifferentiationActual
Match for each functions in List - I to its derivative given in List-II ( array ll List I & List II (A) ⁻¹ ( 2 x 1+x^2 ) & (I) x- x (B) ⁻¹ ( 1-x 1+x ) & (II) -1 1+x^2 (C) e^ ( x+ x) & (III) 2 1+x^2 (D) 1- 2 x (0 < x < 4 ) & (IV) x+ x & (V) - x- x array ) The correct match is
Options
- A( array cccc A & B & C & D III & II & I & V array )
- B( array cccc A & B & C & D II & III & V & IV array )
- C( array cccc A & B & C & D II & III & V & I array )
- D( array cccc A & B & C & D III & II & I & IV array )
Correct answer
D. ( array cccc A & B & C & D III & II & I & IV array )
Step-by-step solution
(A) Let (y= ⁻¹ ( 2 x 1+x^2 ) ) Again, let (x= = ⁻¹ ( 2 1+ ^2 ) ) ( array rlrl & = ⁻¹( 20)=20 & y =2 ⁻¹ x & d y d x = 2 1+x^2 ( differentiating w.r. t. x) array ) (B) Let ( ⁻¹ ( 1-x 1+x )=y ⁻¹(l)- ⁻¹(x)=y ) (0- 1 1+x^2 =y (differentiating w.r.t x ) ) ( y= -1 1+x^2 ) ( B II ) (C) ( aligned e^ ( x+ x) & = x+ x=y y & = x+ x aligned ) Differentiating w.r.t (x ) ( d y d x = x- x ) ( C I ) (D) Let (y= 1- 2 x ) ( aligned & = ^2 x+ ^2 x-2 x x & = ( x- x)^2 y= x- x aligned ) Differentiating w.r. t. (x ), we get ( d y d x = x