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 $e^{10}$.