Proving the Chain Rule

Professor Zap shows how to prove the chain rule using differentials.

Category:

Education

Tags:

• Mathematics
• Calculus
• Chain
• Rule

[abeeraj]

can you make a pre-calculus video for beginners? y knot! (bad nerd jock)

[ProfessorElvisZap]

@abeeraj There is a whole series in two different play lists.

[jasoegaard]

At 9:05 to 9:15 you rewrite (lets use e instead of epsilon): e(k)/h as e(k)/k * k/h

and then look at the limit as h goes to zero.

But since k=g(x0+h)-g(x0) there is a risk that k is zero. In fact if g is a constant

funktion, then k is zero for all values of h.

[ProfessorElvisZap]

@jasoegaard Your point is well taken. If g(x) is a constant, then the issue becomes trivial. Similarly, if e(k) is small in comparison to k, then if k is 0, e(k) must also be 0.

[lamarjlp914]

from 3:45 to 4:10, why is f is a function of y and not x?

[ProfessorElvisZap]

Because its domain will be the range of g. Initially, I wrote it as x_0, and then replaced x_0 with y_0. Indeed, the variable's name does not matter, but observe that I substitute in for y_0=g(x_0) later.

[elizze6]

But isn't the chain rule just fprime(g(x_0)) * gprime(x_0) ? If you multiply it by h then won't that be like multiplying by 0?

[Chewy427]

Woah that is some amazing free hand sketch