L'Hopital's Rule: negative exponential function times a fractional power: Find

.

If we were to substitute directly, we would have the indeterminate form . Hence, we can't yet apply L'Hopital's Rule. If we rewrite the problem as

we now have the form . Now we can apply L'Hopital's Rule. That is, we differentiate the numerator and the denominator separately, take the ratio, and evaluate the limit of the resulting expression. (We do not use the Quotient Rule).

Applying this rule, we get

Carrying out the differentiation, we get