Let
, then
Note that if we had
, then we can consider it as
and we would have
We can combine both the cases to say that if
, then
Basically what this says is that the derivative of the sum or difference of two functions is the sum or difference of the derivatives of the two functions. In fact, we can extend this statement to even three or more functions.
Here are some straight forward examples that employ this differentiation rule.
1. If
, then
2. If
, then
3. If
, then
4. If
, then
5. If
, then