Question

How do you find the slope of the tangent line to the graph of the given function `y=e^-x`?

Answer 1

The slope of the tangent to `y=e^(-x)` is `(-e^(-x))`

Explanation:

The general slope for a function is given by the derivative of the function.

The derivative of `e^x`
`color(white)("XXXX")` `(de^x)/(dx) = e^x`

The derivative of `e^(g(x))`
`color(white)("XXXX")` `(d e^(g(x)))/(dx) = (d g(x))/(d x) * e^(g(x))`

When `g(x) = -x`
`color(white)("XXXX")` `(d g(x))/(d x) = -1`

So `(d e^(-x))/(d x) = (-1) * e^(-x)`