Definition of derivative equation

    • [DOC File]Derivatives - UH

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      The derivative is a calculated quantity that tells you the slope of the tangent line to any point on the graph. The definition of a derivative is taking a limit as h approaches zero, but we’ll use the shortcuts to find them. This is the instantaneous rate of change of the graph at a chosen point.

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    • [DOC File]DERIVATIVES

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      Definition: The derivative of a function f at a point a, denoted by f ′(a), is. provided that the limit exists. If we denote y = f (x), then f ′(a) is called the derivative of f, …

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    • [DOC File]Derivation of the Ordinary Least Squares Estimator

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      In this equation, the only unknowns are the, both the Y and X matrix are know. The Y and X matrix are made up of elements associated with your n-paired observations. Using our knowledge of calculus, we know that if we want to minimize an equation, we can take the first derivative, set the resulting equations equal to zero, and solve for the ...

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    • [DOC File]Derivation of Convection Dispersion Equation for Porous Media

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      So, we can approximate the derivative ∂C/∂t by C/ t or ( 13 ) Finally, we need an expression for the space derivative. Previously we found ( 14 ) and used it to develop an expression for ∂2C/∂t2. This worked well because the result was centered at x. The first order derivative itself though was at x + x/2.

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    • [DOC File]Chapter 3

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      Definition: The derivative of the function with respect to the variable is the function whose value at is , provided it exists. NO ALTERNATE DEFINITION FOR . 1. Consider the function. A. Find . B. Write an equation of the tangent line to the graph of f(x) at and . C. Write an equation …

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    • [DOC File]Derivation of the Ordinary Least Squares Estimator

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      Taking the partial derivative of equation (7) w.r.t. and setting the resulting equations equal to zero, the following first order conditions are obtained: (9) Solving these two equations for the two unknowns, , one obtains the OLS estimates for a and b given the three paired observations. The first equation in equation 9 can be simplified as: (10)

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    • [DOC File]Tangent Lines and Rates of Change

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      We begin with the definition of the derivative, where . Substituting into the derivative formula, Example 2: Find the derivative of and the equation of the tangent line at . Solution: Using the definition of the derivative, Thus the slope of the tangent line at is . For , we can find by simply substituting into . Thus the equation of the ...

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    • [DOC File]Math 151 Handout Example: Using the Definition of the ...

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      Use the definition of the derivative to find if . Solution: Using the limit definition of the derivative, we see that. Example 2: Find the equation of the line tangent to the graph of at the point (0, -1). Solution: To find the equation of any line, including a tangent line, we need to …

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    • [DOC File]Solution of the Diffusion Equation

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      Solution of the Diffusion Equation Introduction and problem definition. ... The derivative on the left is the average (over x) at any time; the derivative on the right is the value at any x for large times. The two equations are consistent. At large times, the derivative at any x has a constant value.

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    • [DOC File]Section 1

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      Using the limit definition of the derivative, we see that Example 5: Find the derivative using the definition and use the result to find the equation of the line tangent to the graph of at the point (0, -1). Solution: To find the equation of any line, including a tangent line, we …

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