Derivative of power function
[DOC File]Section 3
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The original function takes x and computes the second coordinate for the graph point at x. The derivative takes x and computes the instantaneous rate of change of the function at x. Let’s look at a table of these: x Graph point. Slope of tngt l (2 (8 12 (1 (1
[DOC File]3
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The derivative of a linear function. d. The power rule for positive integer powers. e. The constant multiple rule. f. The sum rule. g. The difference rule. 2. When is a piecewise function differentiable? 3. Differentiate the following functions using and citing the rules above: a. f(x)=4-3x7.
[DOC File]New Chapter 3
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The derivative of a linear function. d. The power rule for positive integer powers. e. The constant multiple rule. f. The sum rule. g. The difference rule. 2. When is a piecewise function differentiable? A piecewise function is differentiable, when the entire function is differentiable. Hence, at the “breaking point”, the graph must have ...
[DOC File]3
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Use of implicit differentiation to find the derivative of an inverse function. ... Knowledge of derivatives of basic functions, including power, exponential, logarithmic, trigonometric, and inverse trigonometric functions. Basic rules for the derivative of sums, products, and quotients of functions.
[DOCX File]I. Functions, Graphs, and Limits
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To find the first order partial derivative of the following cubic function, , both the power-rule and sum rule must be applied. The sum rules states we can take the derivative of each component and sum them. The power rule indicates the exponent is placed as a constant and the exponent because the original exponent minus 1.
Derivatives of Power Functions - Problem 1 - Calculus Video by Bri…
The Derivative of a Constant. If where is a constant, then . In other words, the derivative or slope of any constant function is zero. Proof: Example 1: If for all , then for all . We can also write . The Power Rule. If is a positive integer, then for all real values of , .
[DOC File]Derivatives - UH
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The derivative of a function at x is defined as, which can be used to find slopes of tangent lines as well as instantaneous rates of change. Unfortunately, computing the derivative directly from the definition can be quite tedious and overwhelming.
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