How to find instantaneous rate of change for f ( x ) = e x at x=1?

Question

How to find instantaneous rate of change for   f  (  x  )  =      e          x       at x=1?

grubijanebb · Accepted Answer

The instantaneous rate of change is also known as the derivative. It is analogous to the slope of the tangent line at a point, as well.
We might say that the instantaneous rate of change of f at x=a is equal to f'(a).
Here, we have to know that the derivative of

e^{x}

is itself it's a unique and very important function, especially in calculus. That is:

f (x) = e^{x} \Rightarrow f^{'} (x) = e^{x}

So, the instantaneous rate of change of f at x=1 is f'(1), and we see that:

f^{'} (x) = e^{x} \Rightarrow f^{'} (1) = e^{1} = e

The instantaneous rate of change of f at x=1 is e, which is a transcendental number approximately equal to 2.7

Aganippe76 · Accepted Answer

Given:  f  (  x  )  =      e          x       at x=1      d          d      x        (      e          x        )  =      e          x      x=1  (      d          d      x        (      e          x        )  )            |              (      x      =      1      )        =  (      e          x        )            |              (      x      =      1      )        =  eAnswer:  f  (  x  )  =      e          x       at x=1 is e

How to find instantaneous rate of change for

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