Examples of the chain rule
[DOC File]Ex
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Examples. Differentiate the following functions. 1. Answer: 2. Answer: 3. = = = = Answer: 4. = = Answer: Theorem (The Chain Rule) If f and g are two differentiable functions and , then . Proof. By definition, . COMMENT: The Chain Rule tells us how to differentiate the composition of two functions f and g. In this form of the Chain Rule, you would have to identify both functions. Example ...
[DOC File]CALCULUS
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By the Chain Rule, we have . Let and , then . By the alternative form of the Chain Rule, we have (The above example is one of the most common composite functions,, where the outer function is a power function,. The rule for differentiating such function is called the General Power Rule and it can be considered a special case of the Chain Rule.
[DOC File]New Chapter 3
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Use Chain Rule. Let . Differentiate the following functions: Use rule y = ln x ( (vii) Use the product rule: If , then . Let and (viii) Use Chain Rule. Let (ix) Use Chain Rule. Let . 1 . Title: Practice Exercise Sheet 1 Author: cwhelan Last modified by: TCD User Created Date: 10/3/2005 3:49:00 PM Company : …
[DOC File]Practice Exercise Sheet 1 - Trinity College Dublin
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The Chain Rule. Plus. Implicit Differentiation. Higher Order Derivatives. Note. Later in Chapter 7 we will cover. derivatives of . trigonometric functions . and in Chapter 8 . derivatives of . exponential . and . logarithmic functions. The Basic Differentiation Rules. 1. The Constant Rule. If f(x) = c, then . Examples. Find. for the given functions. a) f(x) = 7. b) f(x) = π. 2. The Power Rule ...
The chain rule - explanation and examples - MathBootCamps
Chain Rule - Examples . Chain Rule of Differentiation . Graphing a Composite Function . Hassell's Model . Several examples are presented below to demonstrate the chain rule. Examples show the basic differentiation and applications to extrema in graphing. We also present a couple of applications, including the stability analysis of Hassell's population model and a composite function for ...
[DOC File]Differentiation Rules - Weebly
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Examples 5 and 6 – Differentiate each function. 5. 6. A little generalization.. The Power Rule combined with the Chain Rule. If n is any real number and is differentiable, then. Example 7 – Find if . Example 8 – Differentiate . Examples 9 and 10 – Differentiate each function. 9. 10. Example 11 – Differentiate and simplify using algebra.
[DOC File]AP CALCULUS AB
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While substitution helps us recognize derivatives produced by the chain rule, integration by parts helps us to recognize derivatives produced by the product rule. Grade Level/Subject: The lesson is for 12th graders in AP Calculus. Time: 1-50 minute class period. Purpose: This lesson will give students yet another method of solving complicated integrals. It will also give them a small ...
[DOC File]LESSON X - University of Toledo
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The chain rule tells you how to differentiate such functions. The general chain rule. Another notation for the derivative of a function is . With this notation, the chain rule can be written as follows: Let us consider some examples: In this case, we take and . means here that you take the exponential of . We have and . Let’s apply the chain ...
[DOC File]First year: Basic integration
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Other examples (x2 3)3 is a cubic function of a quadratic function, is a square root function of a quartic function, There are 2 ways to go about solving functions-of-a-function: (i) Chain Rule. If we have y(x) = f (complicated expression), we let u = (complicated expression) then work out and . We then use: The Chain Rule. Examples…
[DOC File]Math 121 - Calculus for Biology I
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Ex. Trigonometric functions with angle nx (sin 5x)′ = (cos 5x)(5x)′ = (cos 5x)∙5 = 5 cos(5x) (csc 4x)′ = (−csc 4x cot 4x)(4x)′ = −4 csc(4x) cot(4x)
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