Question

Please answer all. How do you determine the dose-specific response of a drug given f(x)?

Answer 1

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Just replace in value of x in the function

f(0.1) = 100* (0.1)^2 / ((0.1)^2 + 0.17) = (1)/(0.18) = 5.56

f(0.1) = 5.56

f(0.8) = 100* (0.8)^2 / ((0.8)^2 + 0.17) = (64)/(0.81)= 79.01

f(0.8) = 79.01

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derivative of a quotient

Q(x)= f(x)/g(x)

Q'(x)= (f'(x)*g(x) - f(x)*g'(x)) / (g(x) ^2)

`Q^(\prime)\mleft(x\mright)=(f^(\prime)\mleft(x\mright)\cdot g\mleft(x\mright)-f\mleft(x\mright)\cdot g^(\prime)\mleft(x\mright))/(g\mleft(x\mright)^2)`

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If f(x) = 100* (x^2) / (x^2 + 0.17),

f'(x)= 100 * ( 2x* (x^2 + 0.17) - 2x*x^2 ) / (x^2 + 0.17)^2

f'(x)= 100 * ( 2x^3 + 2x* 0.17 - 2x^3 ) / (x^2 + 0.17)^2

f'(x)= 100 * ( 2x* 0.17 ) / (x^2 + 0.17)^2

f'(x)= 34*x/ (x^2 + 0.17)^2

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Just replace in value of x in the function

f'(0.1)= 34*(0.1)/ (0.1^2 + 0.17)^2

f'(0.1)= 3.4/ (0.18)^2

f'(0.1)= 104.9

f'(0.8)= 34*(0.8)/ (0.8^2 + 0.17)^2

f'(0.8)= 27.2/ (0.81)^2

f'(0.8)= 41.46