Find the derivative of the function. f ( x ) = 1 x 4 a. f ′ ( x ) = − 3 x 5 b. f ′ ( x ) = − 4 x 3 c. f ′ ( x ) = − 4 x 5 d. f ′ ( x ) = − 5 x 5 e. none of the above

Question

Find the derivative of the function.  f  (  x  )  =      1          x      4      a.       f    ′    (  x  )  =  −      3          x      5      b.       f    ′    (  x  )  =  −      4          x      3      c.       f    ′    (  x  )  =  −      4          x      5      d.       f    ′    (  x  )  =  −      5          x      5      e. none of the above

Malcolm Mcbride · Accepted Answer

Step 1  f  (  x  )  =      1          x      4            f    ′    (  x  )  =      d          d      x        (      1          x      4        )  =      d          d      x        (      x          −      4        )  ;      1          a      m        =      a          −      m      Step 2  =  −  4  ⋅      x          −      4      −      1        ;      d          d      x        (      x    n    )  =  n  ⋅      x          x      −      1        =  −  4      x          −      5            f    ′    (  x  )  =            −      4              x      5        (  c  )

Find the derivative of the function. f(x)=1/(x^4)

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