TS EAMCET202410 May 2024Morning ShiftMathematicsDifferentiationActual
If y= ⁻¹ ( 6 x-2 x^2-4 2 x^2-6 x+5 ) then d y d x =
Options
- A2 3 x-x^2-2
- B2 3 x-x^2-2
- C2 2 x^2-6 x+5
- D2 2 x^2-6 x+5
Correct answer
D. 2 2 x^2-6 x+5
Step-by-step solution
y= ⁻¹ ( 6 x-2 x^2-4 2 x^2-6 x+5 ) Let 6 x-2 x^2-4 2 x^2-6 x+5 =v d v d x = 6-4 x (2 x^2-6 x+5 )^2 Now, y= ⁻¹ v d y d x = -1 1-v^2 d v d x aligned & = -1 1- ( 6 x-2 x^2-4 2 x^2-6 x+5 )^2 6-4 x (2 x^2-6 x+5 )^2 & = - (2 x^2-6 x+5 ) (2 x-3)^2 -2(2 x-3) (2 x^2-6 x+5 )^2 = 2 (2 x^2-6 x+5 ) . aligned