Chain Rule

[Silvanoshei]

Trying to understand the Chain Rule of d/dt (5 sin π t +3 cos π t).

I got = 5 cos π t + 3(-sin π t)...

but the proof says = 5 cos π t (π) + 3(-sin π t)(π)

Which flips into = 5 π cos π t - 3 π sin π t

I'm not understanding where the extra (π) came from?

 

[DrPhil]

Trying to understand the Chain Rule of d/dt (5 sin π t +3 cos π t).

I got = 5 cos π t + 3(-sin π t)...

but the proof says = 5 cos π t (π) + 3(-sin π t)(π)

Which flips into = 5 π cos π t - 3 π sin π t

I'm not understanding where the extra (π) came from?

The factor of pi comes from the chain rule.
Since d/dt(sin(u)) = cos(u) du/dt

where u = pi*t, and du/dt = pi

the result is d/dt(sin(pi*t)) = pi*cos(pi*t)