If y=cos-11-logx1+logx then dydxat x=e is
-1e
-12e
12e
1e
Explanation for the correct option.
Step 1. Find the value of dydx.
Differentiate y=cos-11-logx1+logx with respect to x
dydx=ddxcos-11-logx1+logx=-11-1-logx1+logx2(1+logx)-1x-1-logx1x1+logx2
Step 2. Find the value of dydxat x=e.
Put x=ein the above equation.
dydxx=e=-11-1-loge1+loge2(1+loge)-1e-1-loge1e1+loge2=-11-1-11+12(1+1)-1e-1-11e1+12=-11-0-2e-022=-1-12e=12e
Hence, the correct option is C.
If siny+e-xcosy=e then dydxat(1,π) is