Find the derivative of a complicated expression

[stau40]

Homework Statement

Find dP/dt of 2048000(t^2)(e^1600t)+5120t(e^-1600t)+3.2(e^-1600t)

Homework Equations

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.

Thanks in advance!

 

[Samuelb88]

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?