point$($s$)$ possible

The dosage for a certain type of chemotherapy drug depends on several parameters of the particular drug as well as the age, weight, and sex of the patient. For female patients, the formulas giving the dosage for such drugs are $D=0\mathrm{.}85A(c+25)$ and $c=(140-y)\frac{W}{72x},$ where A and x depend on which drug is used, D is the dosage in milligrams $($mg$),$ c is called the creatinine clearance, y is the patient's age in years, and w is the patient's weight in kilograms. Complete parts $($a$)$ through $($e$)$ below.

a$)$ Suppose that a patient is a $55-$year$-$old woman and the drug has parameters $A=4$ and $x=0\mathrm{.}6.$ Use this information to write formulas for $D$ and $c$ that give $D$ as a function of $c,$ and $c$ as a function of $w.$

$D(c)=$

$c(w)=$

$($Simplify your answers. Round to three decimal places as needed.$)$

b$)$ Use your formulas from part $($a$)$ to compute $\frac{dD}{dc}.$

$\frac{dD}{dc}=($Simplify your answer. Round to three decimal places as needed.$)$

c$)$ Use your formulas from part $($a$)$ to compute $\frac{dc}{dw}.$

$\frac{dc}{dw}=($Simplify your answer. Round to three decimal places as needed.$)$

d$)$ Compute $\frac{dD}{dw}.$

Time Remaining: $01$:$17$:$03$