Find the derivative of the function

The derivative of a function f at a point x is denoted as  

There are basic properties and formula we can apply to simplify a function such as the  Product Rule provides the formula:

 For the problem: we let :

 

Now we want to find the derivative of each function.

Recall the power rule for derivatives: 

So, for  , 

Recall that for differentiating exponential functions: 

 where  .

With the function , we get

We now have:

Then following the Product Rule:, we get:

g'(t) = )