If f(x)= x 2 x 3 x and f^ (x)=a( b x)+c( d x)+e( k x) , then the value of (a+c+e)-(b+d+k) equals

Step-by-step solution

aligned f(x) & = x 2 x 3 x & = (2 x 2 x) 3 x 2 & = 1 2 x- 3 x 3 x & = 1 2 [ x 3 x- 3 x 3 x] & = 2 4 x 3 x- 2 4 3 x 3 x & = 1 4 [ 4 x+ 2 x]- 1 4 6 x f^ (x) & = 4 x+ 1 2 2 x- 3 2 6 x f^ (x) & =-4 4 x- 2 x+9 6 x a & =-4, b=4, c=-1, d=2, e=9, k=6 (a & +c+e)-(b+d+k)=4-12=-8 aligned