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[DOC File]Calculus 1 Lecture Notes, Section 4.6
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Integration by substitution is a formal way of performing “the chain rule in reverse.” Big skill: You should be able to calculate integrals using substitution. Let’s say that f(x) is a function that has an antiderivative F(x), which means . and . Now let’s look at what happens when we …
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[DOC File]Chapter 3
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For differentiation we had special rules like chain rule, product rule, and quotient rule. Since integration is the inverse process of differentiation, it seems reasonable to conclude that special rules exist for integration. One special rule we will study for integration is called . …
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[DOC File]LOCAL LINEARITY: SEEING MAY BE BELIEVING
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The Chain Rule . Once students have learned how to differentiate some basic functions, there are fun and interesting ways for them to “discover” the Chain Rule. ... If y is a function of x, say y(x), and if is an antiderivative of and F(y) is an antiderivative of f(y), we can use the Chain Rule to discover that. If we rewrite equation (1 ...
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[DOC File]116Deriv review95 - Saint Mary's College
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The antiderivative rules all come from the derivative rules, but using them is not as straightforward because the chain rule kicks in from the beginning. We use to represent "the general antiderivative of f(x) with x as variable" Since "the general antiderivative" of a derivative is the origional function plus or minus any constant, we have .
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[DOC File]Inverse Functions
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In the special case where the base is since the derivative rule becomes . To generalize, if is a differentiable function of with the use of the Chain Rule the above derivatives take the general form . And if . Derivatives of Exponential Functions. Example 9: Find the derivative of . Solution: Applying the rule for differentiating an exponential ...
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[DOCX File]iblog.dearbornschools.org
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Chain rule. If you have to, guess and check to find the antiderivative (and stay tuned for the next section in the book!). Also, you may have to mathematically manipulate the answer you get in order to match one of the answer choices. Remember, you can multiply a fraction by -1 -1 and not change the value of the fraction.MUST be true.
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[DOC File]Section 1
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The formula for the chain rule was given by: Chain Rule of Differentiation. Suppose we let and let . Then and hence. and . For and we can use these ideas to rewrite the chain rule as follows: This gives another way to write the chain rule, which we summarize as follows: Chain Rule: Alternative Form
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[DOC File]Calculus 1 Lecture Notes, Section 4.1
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antiderivative. of a function f(x) is any function F(x) such that . One of the most common functions to integrate is the power function. To do this, we “run the power rule in reverse”: Power Rule for taking derivatives: Power Rule “in reverse” for taking antiderivatives: Example: find the derivative of . …
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[DOCX File]www.lcps.org
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More chain rule and implicit differentiation intuition. Trig Implicit Differentiation Example. Calculus: Derivative of x^(x^x) Introduction to L'Hopital's Rule. L'Hopital's Rule Example 1. L'Hopital's Rule Example 2. L'Hopital's Rule Example 3. Maxima Minima Slope Intuition. Inflection Points and Concavity Intuition. Monotonicity Theorem ...
chain rule for integral

Antiderivative chain rule