1. ## Application of derivative about life science

Can anybody help me check out if I got the right answer? also how can I address the unit of part b!~

Thanks!!!!~

When a certain drug is injected into a muscle, the muscle responds by contracting. The amount of contraction , s(in millimeters) is related to the concentration of drug, x (in millimeters)by

s(x)= x/(m+nx) where m and n are constants.

a)Find s'(x)

S'(x)=m/((m+nx)^2)

b)Find the rate of contraction when the concentration of the drug is 50ml,m=10 and n=3

s'(50)=10/((10+30*50)^2)=3.9*10^(-4) units?

as for this one how can I address the unit of the rate of contraction?

2. Originally Posted by shannon1111
Can anybody help me check out if I got the right answer? also how can I address the unit of part b!~

Thanks!!!!~

When a certain drug is injected into a muscle, the muscle responds by contracting. The amount of contraction , s(in millimeters) is related to the concentration of drug, x (in millimeters)by

s(x)= x/(m+nx) where m and n are constants.

a)Find s'(x)

S'(x)=m/((m+nx)^2)

b)Find the rate of contraction when the concentration of the drug is 50ml,m=10 and n=3

s'(50)=10/((10+30*50)^2)=3.9*10^(-4) units?

as for this one how can I address the unit of the rate of contraction?
s'(x) ... mm/mL

3. I am confused about the units, how can I adress the units of all the derivatives problem?

4. Originally Posted by shannon1111
I am confused about the units, how can I adress the units of all the derivatives problem?
$\displaystyle \frac{dy}{dx}$ ... $\displaystyle \frac{units \, of \, the \, dependent \, variable}{units \, of \, the \, independent \, variable}$

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### derivative calculus in muscle contraction

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