What is the derivative of e^-x?

The derivative of e^-x is -e^-x. The derivative of e^-x is found by applying the chain rule of derivatives and the knowledge that the derivative of e^x is always e^x, which can be found using a more complicated proof.

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.