Calculating the Slope of $y=e^x$ at $x=10$
The question asks for the slope of the function $y = e^x$ at the specific point $x = 10$. The slope of a function at any given point is found by calculating its derivative and evaluating it at that point.
Finding the Derivative
First, determine the derivative of the function $y = e^x$. The derivative of the natural exponential function $e^x$ with respect to $x$ is $e^x$.
The derivative is:
$ \frac{dy}{dx} = \frac{d}{dx}(e^x) = e^x $
Evaluating the Slope
Next, evaluate the derivative at the specified value $x = 10$. This gives the slope of the function at that point.
Slope $= \frac{dy}{dx}\Big|_{x=10} = e^{10}$
Result
Thus, the slope of the function $y = e^x$ when $x = 10$ is $e^{10}$.
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