Use implicit differentiation to find the derivative of y = arccos ⁡ ( x ) as a function of x and say where this derivative is defined.Don't really get the concept of implicit differentiation.

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Use implicit differentiation to find the derivative of   y  =  arccos  ⁡      (                  x              )   as a function of x and say where this derivative is defined.Don&#039;t really get the concept of implicit differentiation.

diamondogsaz · Accepted Answer

y  =  arccos  ⁡      x    x  =      cos    2    ⁡  y            d      x              d      x        =      d          d      x        (      cos    2    ⁡  y  )  1  =      d          d      y        (      cos    2    ⁡  y  )  ⋅            d      y              d      x        1  =  (  2  )  (  cos  ⁡  y  )  (  −  sin  ⁡  y  )  ⋅            d      y              d      x                  d      y              d      x        =  −      1          2      cos      ⁡      y      sin      ⁡      y        =  ±      1          2              x        (        1        −        x        )            Now think about where that is defined (when is the denominator nonzero?).

therightwomanwf · Accepted Answer

y  =  arccos  ⁡  (      x    )      ⟺      cos  ⁡  y  =      x  now you can use implicit differentiation to find             d      y              d      x      :  −  sin  ⁡  (  y  )            d      y              d      x        =      1          2              x              ⇒            d      y              d      x        =  .  .  .  .

Use implicit differentiation to find the derivative of y=arccos sqrt(x) as a function of x and say where this derivative is defined. Don't really get the concept of implicit differentiation.

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