Main Points
For a function y = f(z) and z = g(t), { y = f(g(t)) }, a change in 't' affects z in turn affecting y and the derivative can thus be computed with the formula: dy/dt = dy/dz * dz/dt. In other words: d/dt(f(g(t))) = f '(g(t))*g '(t).
Challenges
I do not understand how we move from this formula: dy/dt = dy/dz * dz/dt, to this one: d/dt(f(g(t))) = f '(g(t))*g '(t). What exactly is the connection between the two?
Reflections
Being able to differentiate compositre functions allows one to take into consideration the further effects of an event rather than only the immediate one. Again facilitating the possiblity of having future plans. Applied calc seems so far to simply be facilitating predictions.
Subscribe to:
Post Comments (Atom)
No comments:
Post a Comment