Given: [ tan − 1 ⁡ ( x ) ] 2 + [ cot − 1 ⁡ ( y ) ] 2 = 1Find the tangent line equation to the graph at the point (1,0) by implicit differentiationI found the derivative: d y d x = 4 tan − 1 ⁡ ( x ) ⋅ cot − 1 ⁡ ( y ) ( y 2 + 1 ) ( x 2 + 1 ) I may have done my derivative wrong, but my main concern is at some point 0 will be plugged into cot inverse, resulting in division by zero.

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Given:  [      tan          −      1        ⁡  (  x  )      ]    2    +  [      cot          −      1        ⁡  (  y  )      ]    2    =  1Find the tangent line equation to the graph at the point (1,0) by implicit differentiationI found the derivative:                    d        y                    d        x              =                    4                  tan                      −            1                          ⁡        (        x        )        ⋅                  cot                      −            1                          ⁡        (        y        )                    (                  y          2                +        1        )        (                  x          2                +        1        )            I may have done my derivative wrong, but my main concern is at some point 0 will be plugged into cot inverse, resulting in division by zero.

pokajalaq1 · Accepted Answer

2                  tan                      −            1                          ⁡        x                    1        +                  x                      2                                    d    x    −                  2                  cot                      −            1                          ⁡        y                    1        +                  y                      2                                    d    y    =    0                      d        y                    d        x              =                  (        1        +                  y                      2                          )                  tan                      −            1                          ⁡        x                    (        1        +                  x                      2                          )                  cot                      −            1                          ⁡        y            Note that (1,0) doesn&#039;t lie on the graph.The graph can be parametrized as   (  x  ,  y  )  =  (  tan  ⁡  cos  ⁡  t  ,  cot  ⁡  sin  ⁡  t  )

Given: [tan^(−1)(x)]^2+[cot^(−1)(y)]^2=1 Find the tangent line equation to the graph at the point (1,0) by implicit differentiation

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