Manipal MET2020MathematicsDifferentiation
Let f(x)= | array ccc 3 x & 1 & 2 ( 3 x 2 + 3 x 2 )^2 3 x & -1 & 2 ( ^2 3 x 2 - ^2 3 x 2 ) 3 x & 4 & 1+2 3 x array | Then, the value of f^ (x) at x=(2 n+1) , n I (the set of integers) is equal to
Options
- A(-1)^n
- B(-1)^ n+1
- C3
- D9
Correct answer
C. 3
Step-by-step solution
Given, f(x)= | array ccc 3 x & 1 & 2 ( 3 x 2 + 3 x 2 )^2 3 x & -1 & 2 ( ^2 3 x 2 - ^2 3 x 2 ) 3 x & 4 & 1+2 3 x array |f^ (x)= | array ccc d d x ( 3 x) & 1 & 2 ( 3 x 2 + 3 x 2 )^2 d d x ( 3 x) & -1 & 2 ( ^2 3 x 2 - ^2 3 x 2 ) d d x ( 3 x) & 4 & 1+2 3 x array |+ | array ccc 3 x & d d x (1) & 2 ( 3 x 2 + 3 x 2 )^2 3 x & d d x (-1) & 2 ( ^2 3 x 2 - ^2 3 x 2 ) 3 x & d d x (4) & 1+2 3 x array |+ | array ccc 3 x & 1 & 2 d d x ( 3 x 2 + 3 x 2 )^2 3 x & -1 & 2 d d x ( ^2 3 x 2 - ^2 3 x 2 ) 3 x & 4 & d d x (1+2 3 x) array |