Preparing the for the chain rule
Chain Rule for Powers
See the explanation of mathematical
induction. in Three Skills for Algebra.
Theorem (Chain Rule for Powers): If p(y) = yk
for some whole number k, and z = p(y) where y = g(x). Then z' = p '(y)
g'(x). Proof:
Apply Mathematical Induction to k in the set of natural numbers N = {0, 1, 2,
3, ... . Use the product rule repeatedly. See details in proof below.If
you did not understand the proof above, the following is a real player
presentation:
[Play Video]
4¼ minutes: Why d/dx (un) = n un-1
du/dx - Proof by mathematical induction.
(Chain-Rule for Powers)
Video Examples (Real Player)
- [Play
Video] 1 minutes: 1st Example using rule d/dx
(un) = n un-1 du/dx -
- [Play
Video] 1¾ minutes: 2nd Example using rule d/dx
(un) = n un-1 du/dx -
- [Play
Video] 1¾ minutes: 3rd Example using rule d/dx
(un) = n un-1 du/dx -
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Calculus Chapters
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Starter Guide (Views)
Real Player Videos
3. Derivative Motivation
3. Derivative Definition I
3. Derivatives Definition II
3. Calculus: Why Radians
3 d/dx of sin(x) & cos(x) (I)
3 d/dx of sin(x) & cos(x) (II)
3.Sum Rule
3. Product Rule
3. Power Rule
3. Previous Rules Combined
3. d/dx for Polynomials
3. Reciprocal Rule
3. Reciprocal Law: sec & csc
3. Reciprocals & Power Rule
3. Power Law for Integers < 0
3. Quotient Rule
3. Quotient Rule Examples
3. Quotient Rule: tan & cot
3. Linear Chain Rule
3. Chain Rule for Powers
3. Chain Rule - Polynomials
3. Chain Rule Examples I
3. Chain Rule Examples II
3. Linear Approximation I
3. General Chain Rule
3. Inverse Fns Derivatives
3. Chain Rule: ln(x) & exp(x)
3. Square & Cube Roots
YOU are better than YOU think. Show yourself how:
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Logic
Mastery
Amazing, Amusing, Amorous, Delicious, Delightful, Edifying,
Strengthening Elixir.
It eases work & learning difficulties Makes the hard easier. Opens eyes.
Leads to greater precision.
in reading and
writing
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Caution: Site advice is approximately
correct, for some circumstances, not all. . That leaves room for thought and
refinement.. |
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