elnx = x is another way of saying that y = ex and y = lnx are inverse functions.
Inverse functions have reciprocal derivatives at their corresponding (x, y) → (y, x) values.
If f(x) has coordinate point (a, b).
And if g(x) is the inverse of f(x),
Let f(x) = ex and g(x) = lnx.
First find f '(x) = _____. (This should be easy!)
To find g'(x), take the reciprocal of f '(x), but NOT at the
Now evaluate g'(x) when f(x) = ex.