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

1 Answer
Alan P.
Jun 25, 2015

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)

Related questions
See all questions in Tangent Line to a Curve
Impact of this question
1275 views around the world
You can reuse this answer
Creative Commons License