Derivatives

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Students will demonstrate an understanding of the definition of the derivative of a function at a point, and the notion of differentiability.
Demonstrate an understanding of the derivative of a function as the slope of the tangent line to the graph of the function
Demonstrate an understanding of the interpretation of the derivative as instantaneous rate of change
Use derivatives to solve a variety of problems coming from physics, chemistry, economics, etc that involve the rate of change of a function
Demonstrate an understanding of the relationship between differentiability and continuity.
Use derivative formulas to find the derivatives of algebraic, trigonometric, inverse trigonometric, exponential, and logarithmic functions.
Students will apply the rules of differentiation to functions.
Use the Chain Rule and applications to the calculation of the derivative of a variety of composite functions
Find the derivatives of relations and use implicit differentiation in a wide variety of problems from physics, chemistry, economics, etc.
Demonstrate an understanding of and apply Rolle's Theorem, the Mean Value Theorem.
Students will explore the continuity of functions of two independent variables in terms of the limits of such functions as (x, y) approaches a given point in the plane.
Students will explore, find, use, and apply partial differentiation of functions of two independent variables of the form z = f(x, y) and implicit functions of the form f(x, y, z) = 0.
Approximate the partial derivatives at a point of a function defined by a table of data
Find expressions for the first and second partial derivatives of a function
Define and apply the total differential to approximate real world phenomena
Represent the partial derivatives of a system of two functions in two variables using the Jacobian
Find the partial derivatives of the composition of functions using the general chain rule.
Apply partial differentiation to problems of optimization, including problems requiring the use of the Lagrange multiplier.
Students will define and apply the gradient, the divergence, and curl in terms of differential vector operations.

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