Question #e365f
1 Answer
Same as you would if the exponent were positive - with a slight adjustment for the chain rule.
Explanation:
Consider differentiating
It's a special function because its derivative is itself. Now, try
We see that the derivative is the same as itself again - except this time, it's negative. Why?
The answer has to do with the chain rule, which states that the derivative of a composite function (a function within a function) is the derivative of the inner function times the derivative of the function in general. This is best demonstrated with an example:
We have one function,
Because
The same logic holds for functions with negative exponents, like
This makes intuitive sense too. We know that
So for
In this case