logarithmic differentiation ...
take the derivative w/r to x ...
Yes, you can, using the chain rule.
By the way, here's an interesting point: if , where f and g are integrable functions, there are two common mistakes in finding the derivative:
1) Ignore the fact that g is a variable and use the power law:
2) Ignore the fact that f is a variable and treat it as an exponential:
As I said, those are both wrong. The correct derivative is the sum of those!