derivatives 25 videos

The Derivative Function
Calculus The Derivative
How to define the derivative function f'(x).
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Derivatives of Power Functions
Calculus The Derivative
How to determine the derivative of a power function.
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Derivatives of Polynomial Functions
Calculus The Derivative
How to compute the derivative of a polynomial function using two properties of the derivative.
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Derivatives of Exponential Functions
Calculus The Derivative
How to use the definition of the derivative to find a derivative formula for exponential functions.
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Derivatives of Linear Functions
Calculus The Derivative
How to determine the derivative of a linear function.
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Derivative Notation
Calculus The Derivative
How to recognize and use Newton's and Leibniz's notation for the derivative.
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Derivatives of Logarithmic Functions
Calculus The Derivative
How to infer the derivative of the natural log function using a calculator investigation.
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The Definition of the Derivative
Calculus The Derivative
How to define the derivative of a function at a point x=a.
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Curve Sketching with Derivatives
Calculus Applications of the Derivative
How to evaluate the limit of a function using continuity.

Antidifferentiation
Calculus Antiderivatives and Differential Equations
How to find an antiderivative of a function.
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Economics: Marginal Cost & Revenue
Calculus Applications of the Derivative
How to interpret the derivatives of the cost and revenue functions as marginal cost and marginal revenue.
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Optimization Using the First Derivative Test
Calculus Applications of the Derivative
How to evaluate the limit of a function as x goes to infinity (or minus infinity), and how to determine the horizontal asymptote of its graph.

Optimization Using the Second Derivative Test
Calculus Applications of the Derivative
How to compute the average velocity of an object moving in one dimension from a graph of its position vs. time.

Definition of Antiderivatives
Calculus Antiderivatives and Differential Equations
How to define an antiderivative.
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Differential Equations
Calculus Antiderivatives and Differential Equations
How to solve simple differential equations.
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The Product Rule
Calculus Techniques of Differentiation
How to differentiate a product of two functions.
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The First Derivative Test for Relative Maximum and Minimum
Calculus Applications of the Derivative
How to use an algebraic approach to find onesided limits of a rational function, and how these limits can be used to find a vertical asymptote.

The Second Derivative Test for Relative Maximum and Minimum
Calculus Applications of the Derivative
How to show that polynomial functions are continuous functions.

The Quotient Rule
Calculus Techniques of Differentiation
How to differentiate a quotient of two functions.
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The Method of Substitution
Calculus Antiderivatives and Differential Equations
How to evaluate an indefinite integral using the method of substitution.
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