If y=tan-1a-x1+ax, then dydx=
12x(1+x)
1x(1+x)
-12x(1+x)
None of these
Explanation for the correct option.
Find the value of dydx.
Using the identity tan-1x-y1+xy=tan-1x-tan-1y, the equation y=tan-1a-x1+ax can be written as:
y=tan-1a-x1+ax⇒y=tan-1a-tan-1x
Now differentiate it with respect to x.
dydx=ddxtan-1a-tan-1x=0-11+x212x=-12x(1+x)
Hence, the correct option is C.