How to differentiate ln ( ( sin 2 ) x ) ?

Question

How to differentiate             ln              (                  (                      sin            2                    )                x        )            ?

Julien Zavala · Accepted Answer

ln              (                              sin            2                    x                )              =          ln              (                              (                          sin              x                        )                    2                )              =    2          ln              (                  sin          x                )            Next, we use             d              d        x                    (              ln        u            )        =          1      u        d          u              d        x            , to get            d              d        x                    (              ln                  (                                    sin              2                        x                    )                    )        =    2          d              d        x                    (              ln                  (                      sin            x                    )                    )            =    2          (              1                  sin          x                    )        ⋅          d              d        x                    (              sin        x            )            =    2          (              1                  sin          x                    )              (              cos        x            )      Hence, answer is       =    2          cot      x

datgeni5quc · Accepted Answer

y    =          ln              (                              (                          sin              x                        )                    2                )            Which means that:            e      y        =                  (                  sin          x                )            2      Use implicit differentiation on the left hand side of the equation and the chain rule on the right hand side of the equation:            e      y        ⋅                            d          y                                      d          x                      =    2          sin      x        ⋅          cos      x      Divide expressions on both sides of the equation by             e      y      :                              d          y                                      d          x                      =                  2                  sin          x                ⋅                  cos          x                            e        y            Don&#039;t forget that             e      y       is                     (                  sin          x                )            2      :                              d          y                                      d          x                      =                  2                  sin          x                          cos          x                                      sin          x                          sin          x                    Simplify the fraction above:                              d          y                                      d          x                      =    2    ⋅                  cos        x                    sin        x                                cos        x                    sin        x             is cot x:                              d          y                                      d          x                      =    2          cot      x

How do you differentiate ln((sin^2)x)?

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