Let  y be an implicit function of  x defined by  x2x−2xxcoty−1=0 . Then y'1 equals to

x2x−2xxcoty−1=0→1 At x=1, we have 1−2cot⁡y−1=0⇒cot⁡y=0∴y=π/2 Differentiating (1) w.r.t. x, we have 2x2x(1+log⁡x)−2xx−cosec2⁡ydydx+cot⁡yxx(1+log⁡x)=0 At P(1,π/2), we have 2(1+log⁡1)−21(−1)dydxp+0=0⇒2+2dydxp=0.∴dydxp=−1