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

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Answer 1 · 2016-11-23T04:52:14

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:

$f(x)=e^x" "=>" "f'(x)=e^x$

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

$f'(x)=e^x" "=>" "f'(1)=e^1=e$

The instantaneous rate of change of $f$ at $x=1$ is $e$ , which is a transcendental number approximately equal to $2.7182818$ .

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