What Is the Derivative of E^-X?

The chain rule of derivatives states that a composite function's derivative can be found by multiplying the inside function's derivative and the outside function's derivative. In this example, the larger function is e, and the inside function is -x. The outside function's derivative in this case is e^-x, and the inside function's derivative is -1. When multiplied, these give a resulting derivative of -e^-x.