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2(x+3)/(x+1)
One can treat complex multiplication as polynomial multiplication, but remembering i^2 = -1. To perform polynomial multiplication, multiply each term one by one, then add them together. Hence (3+i)(1+2i) ...
This question is a typical example aimed to test the student's understanding of the quotient rule, a technique which is used very often in calculus problems. Answer: For a function f(x) = cosx/sinx = u/v,...
We can identify xe^(-2x) as a product and hence we will most probably need to use integration by parts.
We then set u = x and v' = x^(-2x). It is important to do it this way round so that when we d...
The rules to know are 1) when differentiating e to the power of x... be it 2x or 100x... you bring down the number in front of x, and leave the power as it is. in our case e^(2x) goes to 2e^(2x).
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