What is the derivative of ∴ d y d x = - cot x csc x ?

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What is the derivative of       ∴                  d        y                    d        x              =    -          cot      x              csc      x      ?

Gerald Dickerson · Accepted Answer

Since             f              (        x        )              =          1                        sin                      (            x            )                                =          csc              (        x        )            , the answer can be written down from memorization that       f    ′          (      x      )        =    -          csc              (        x        )                    cot              (        x        )            .Alternatively, the Quotient Rule can be used:      f    ′          (      x      )        =                            sin                      (            x            )                          ⋅        0        -        1        ⋅                  cos                      (            x            )                                                            sin                          2                                            (            x            )                                =    -                            cos                      (            x            )                                                            sin                          2                                            (            x            )                                    =    -                  1                              sin                      (            x            )                                ⋅                            cos                      (            x            )                                                sin                      (            x            )                                =    -          csc              (        x        )                    cot              (        x        )

What is the derivative of ∴ d y d x = - cot x csc...

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