If y=1+1x1+2x1+3x….1+nx and x≠0, then dydx where x=-1 is:
n!
n-1!
-1nn-1!
-1nn!
Explanation for the correct option.
It is given that y=1+1x1+2x1+3x….1+nx.
Differentiating w.r.t x, we get
dydx=-1x21+2x1+3x….1+nx+-2x21+1x1+3x….1+nx+...+1+1x1+2x1+3x...-nx2byproductrule
By substituting x=-1, we get
dydx=-1-1-2….1-n+-20-2….1-n+...+0-1-2...-n=-1-1-2….1-nasallothertermswillbe0=-1n1·2·3·......·n-1=-1nn-1!
Hence, option C is correct.