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Derivative of a Constant: Examples with Video - Calculus ...
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 , .
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[DOC File]Worksheet on Derivatives
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Marginal utilities are measured while all other goods are held constant. Thus, marginal utility of X is a partial derivative of U with respect to X. The quantities of all other goods are held constant. Example: Let . be the utility function. A partial derivative with respect to X ignores all variables other than X and treat them as if they are ...
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[DOC File]DERIVATIVES
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RULE 4: Derivative of a constant times a power function: f(x) = k*x^n, where n is a positive integer and k is a constant. Consider f(x) = 5*x^1, f(x) = 7/3*x^2, f(x) = -2*x^3, etc. #11. Use Maple, or RULE 1, to find the derivative of f(x) = k*x^1: f '(x) = _____ . #12. Use Maple to find the derivative of f(x) = k*x^2: f …
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[DOC File]Section 3
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Derivative of a Constant Function. Suppose we have a function . Graph the function: The slope of a tangent line to any point on the graph would be _____. So: Power Functions. Now, let’s look at functions that take the form , where n is a positive integer. If n = 1, then , which is the function y = x, so . Proof:
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[DOC File]lab9.mws - [Server 1]
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Since the derivative of a constant times a function is the constant times the derivative of the function we obtain the following derivatives for each of the terms. To find we need to treat x as a constant and take the derivative of f(x,y) with respect to y, thus we need to find. Taking each of these derivatives we get the following.
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[DOC File]Chapter 10 Multi-Variable Functions
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Our derivative function is f’(x) = 3, so it is just a flat line. What would happen if y = constant, say 2? Would f(x+h)=f(x)? So what is the slope of a flat line? Let’s try another. Let’s find the derivative function of f(x) = x2-x. What is f(x+h)? If I plug the value x=2 into 2x-1 I get 3. What does that 3 mean?
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[DOC File]AP CALCULUS AB
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Therefore, any linear function has a constant derivative equals to the slope of its graph, which is a line of slope m. It says that the instantaneous rate of change of a linear function is constant, and that the tangent line to the graph of a line is always the line itself (because the tangent line has the same slope as the line, and they ...
derivative of 1

Derivative of a constant function