# Find the derivative of a complicated expression

1. Sep 7, 2010

### stau40

1. The problem statement, all variables and given/known data
Find dP/dt of 2048000(t^2)(e^1600t)+5120t(e^-1600t)+3.2(e^-1600t)

2. Relevant equations

3. The attempt at a solution
2048000(2t(e^-1600t)-1600(t^2)(e^-1600t))+5120((e^-1600t)-1600(e^-1600t))+3.2(-1600(e^-1600t))
After moving the t over to simply the first part and multiplying thru I get:
4096000t-3276800000(t^2)+5120-8192000-5120(e^-1600t)

Can this be correct? For some reason it seems like I did something wrong, but I keep checking the numbers and can't figure out what it could be.

The way you have presented your question is rather confusing so I am going to assume a function P(t) is equal to 2048000(t^2)(e^1600t)+5120t(e^-1600t)+3.2(e^-1600t). The trick to differentiating these kind of 'functions' is to really do it in parts, at least until you're comfortable using all the rules of differentiation. For example, try letting f(t) = 2048000(t^2), and g(t) = (e^1600t), then determine [f(t)g(t)]. Next, let h(t) = 5120t, and p(t) = e^-1600t, then determine [h(t)p(t)]. And of course, at last, take the derivative of the last term. So your derivative dP/dt = [f(t)g(t)] + [h(t)p(t)] + 3.2[e^-1600t]`. You can do this because the linearity of the derivative operation. At any rate, make sense?