derivative implementation?

Question

If f(t) is the quantity in kilograms of a chemical produced after t minutes and g(t) is the quantity in kilograms produced agter t seconds then f ' (t) = 60 g ' (t)

Is this statement correct?

f ' (t) means the derivative of the function f(t) and
g ' (t) means the derivative of the function g(t)

Please tell me on how would you proof this

Answer 1

It is not correct.
f(t) <> 60*g(t)

the correct represntation is
f(T) kg permin where T is time in miniutes

g(t) kg/sec where t is time in secs

where T = t/60


now you know the difference

also not g(t) is not constant between one miniute to another. so you cant multiply by 60

Answer 2

Your hypothesis can be written as:

f(t) = g(60 * t)

Using the chain rule:

f'(t) = g'(60 * t) * 60

Therefore the thesis is true for t<>0 only if g'(t)=g'(60*t), which means g'(t) being constant, which is the same as to say that the chemical reaction has constant speed. If that is not so, then the statement is incorrect.

Answer 3

First of all, both f(t) and g(t) have to be functions. By differentiating f(t) and g(t), what you got is the slope of the function, or the rate of reaction in ur case.

we have to convert the time into _the same unit_, otherwise we are comparing oranges to apples :) So, say f(t) = kt+ b, and g(t) = wt + a, both t in seconds. As long as k and w stay the same, the statement is false.