There is a derivation in my economics textbook: Romer - advanced macroeconomics, that he doesn't explain and I can't see why it works:

He says that:

\(\displaystyle f(t) = \int_{y=0}^t r(y)dy \)

And concludes that:

\(\displaystyle \delta f(t)/\delta t = r(t)\)

Could someone point me to the rule that allows you to do this, so that I can study it?

Edit:

I have a similar problem with the following equation:

\(\displaystyle g(t) = \int_{t=0}^\infty a*c(t)^{1-\theta}dt \)

How do you calculate the following:

\(\displaystyle \delta g(t)/\delta t\)

He says that:

\(\displaystyle f(t) = \int_{y=0}^t r(y)dy \)

And concludes that:

\(\displaystyle \delta f(t)/\delta t = r(t)\)

Could someone point me to the rule that allows you to do this, so that I can study it?

Edit:

I have a similar problem with the following equation:

\(\displaystyle g(t) = \int_{t=0}^\infty a*c(t)^{1-\theta}dt \)

How do you calculate the following:

\(\displaystyle \delta g(t)/\delta t\)

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