How would I solve this equation for x?
0=3.9657(0.9982^x)ln0.9982
as written, there is no solution.
If the product of some numbers is 0, then one of the numbers must be zero.
3.9657 ≠ 0
ln 0.9982 ≠ 0
0.9982^x is never zero
Looks like you have written
d/dx (3.9657 * 0.9982^x)
care to clarify what you really want?