How do you find the instantaneous slope of y = 1 x at x=4?

Question

How do you find the instantaneous slope of   y  =      1    x   at x=4?

Leland Ochoa · Accepted Answer

The instantaneous slope is determined by differentiating y at x=4
Differentiating y is computed by applying the quotient rule

(\frac{u}{v})^{'} = \frac{u^{'} v - v^{'} u}{v^{2}}

y = \frac{1}{x}

y^{'} = \frac{1^{'} \times x - x^{'} \times 1}{x^{2}}

y^{'} = 0 - \frac{1}{x^{2}}

y^{'} = - \frac{1}{x^{2}}

y_{(x = 4)}^{'} = - \frac{1}{4^{2}} = - \frac{1}{16}

Therefore, the slope of y at x=4 is

- \frac{1}{16}

Kapalci · Accepted Answer

f  (  x  )  =      1    x        ﻿    ,  x  =  4      d          d      x        (      1    x    )  =  −      1          x              2              (      d          d      x        (      1    x    )  )            |              (      x      =      4      )        =  (  −      1          x              2              )            |              (      x      =      4      )        =  −      1    16    f  (  x  )  =      1    x    a  t  x  =  4  i  s  −      1    16

How do you find the instantaneous slope of

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