# Time derivative

• May 18th 2009, 02:37 PM
kepler
Time derivative
Hi,
I have the following problem: I have a function to evaluate the obliquity of the ecliptic (astronomy) in the form:
Code:

`f(t) = a + bt + ct^2 + dt^3`
Its derivative (rate) is:
Code:

`derivative of f(t) = b + 2ct + 3dt^2`
Everything works out until here. But I've improved the formula; but now the t factor is equal to t/100;let's call it t', and with the new coefficients a', b', c' and d':
Code:

`f_2(t') = a' + b't' + c't'^2 + d't'^3`
If I calculate f_2 for a given t the result is the same, but improved. But what about the derivative of f_2? It's:
Code:

`derivative of f_2(t') = b' + 2c't' + 3d't'^2`
The rate, or derivative is referred to t' = t / 100; to referrer it to t, must I divide de derivative of f_2 by 100?
Kind regards,
Kepler
• May 19th 2009, 07:11 AM
HallsofIvy
Quote:

Originally Posted by kepler
Hi,
I have the following problem: I have a function to evaluate the obliquity of the ecliptic (astronomy) in the form:
Code:

`f(t) = a + bt + ct^2 + dt^3`
Its derivative (rate) is:
Code:

`derivative of f(t) = b + 2ct + 3dt^2`
Everything works out until here. But I've improved the formula; but now the t factor is equal to t/100;let's call it t', and with the new coefficients a', b', c' and d':
Code:

`f_2(t') = a' + b't' + c't'^2 + d't'^3`
If I calculate f_2 for a given t the result is the same, but improved. But what about the derivative of f_2? It's:
Code:

`derivative of f_2(t') = b' + 2c't' + 3d't'^2`
The rate, or derivative is referred to t' = t / 100; to referrer it to t, must I divide de derivative of f_2 by 100?
Kind regards,
Kepler

Yes, the derivative with respect to t' is [itex]b'+ 2c't+ 3d't'^2[/itex]. Now, by the chain rule, to get the derivative with respect to t, multiply by the derivative of t' with respect to t. Since t'= t/100, that is 1/100.