I need some assistance on several problems I am absolutely stuck on:

1.

"The quantity of a drug, Q mg, present in the body t hours after the injection of the drug is given is:

Q=f(t)=80te^-0.38t

find:

f(1)=54.71

f'(1)=______

f(6)=49.10

f'(6)=______

Round your answers to two decimal places."

I know I'd find the derivative of f(t). Would it be:

80t(-.38t)e^-.38t

?

2nd question:

"A dose, D, of a drug causes a temperature change, T, in a patient. For C a positive constant, C=32, T is given by:

T=((C/2)-(D/3))D^3

What is the rate of change of temperature change with respect to dose?

dT/dD=_____

For what doses does the temperature change increase as the dose increases?

D < _____"

Not sure where to start here. Maybe substitute C=32 and take the derivative of the equation?

3rd:

(describes a museum deciding to sell a painting and invest the proceeds)

basically:

"B(t)= P(t)(1.04)^(10-t)"

{where P(t)=sale price, B(t)=balance in yr. 2010, t=year when painting is sold, measured from the year 2000 so 0<t<10}

"Find B'(7), given that P(7)=120,000 and P'(7)=5,000.

B'(7)= _____

Round your answer to two decimal places."

I have tried finding the derivative of the equation {B'(t)=P(t)ln(1.04)(1.04)^(10-t)}

and evaluating for t=7, but that didn't work. Any other ideas?

Last question:

"Given r(2) = 16, s(2) = 3, s(4) = 4, r'(2) = 9, s'(2) = 2, and s'(4) = 9, compute the following derivatives, or state what additional information you would need to be able to compute the derivative.

(a.)H'(2) if H(x) = r(x) + s(x)

H'(2)=11

(b.)H'(2) if H(x) = 8s(x)

H'(2)=16

(c.)H'(2) if H(x) = r(x) * s(x)

H'(2)= _____

(d.)H'(2) if H(x) = sqrt(r(x))

H'(2)= _____"

Is something missing from (c) and (d) that I need? I've tried for (c):

16*3

9*2 (r'(x)*s'(x)=H'(x)?)

and (just a big guess) r(s(x))

and for (d):

256 (r(x)^2)

3 (sqrt(r'(x)))

4 (sqrt(r(x)))

but none of these worked out.

I hate to be asking so many questions in one post, but I am at a complete loss for where to go based on what I have already tried. Any help is (as always) highly appreciated!