How do I find the derivative of two functions multiplied by each other?

To find the derivative of two functions multiplied by each other we would use the product rule.

The product rule: (fg)'(x) = f '(x).g(x) + f(x).g'(x)

First we need to split our function into the two parts that are multiplied by eachother, and label these f and g. For example, h(x) = sin(x)(2x + 1)

For this we would label f(x) = sin(x) and g(x) = (2x + 1)

Now we need to find the derivatives of these, to use in the above formula:

f '(x) = cos(x)  g'(x) = 2

So then we put these together in the formula above to get our answer as follows:

h'(x) = cos(x)(2x + 1) + 2sin(x)