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Applications of derivatives

Meaning of the derivative in context

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Interpreting the meaning of the derivative in context
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Analyzing problems involving rates of change in applied contexts
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Interpreting the meaning of the derivative in contextGet 3 of 4 questions to level up!

Straight-line motion

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Introduction to one-dimensional motion with calculus
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Interpreting direction of motion from position-time graph
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Interpreting direction of motion from velocity-time graph
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Interpreting change in speed from velocity-time graph
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Worked example: Motion problems with derivatives
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Total distance traveled with derivatives
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Interpret motion graphsGet 3 of 4 questions to level up!
Motion problems (differential calc)Get 3 of 4 questions to level up!

Non-motion applications of derivatives

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Applied rate of change: forgetfulness
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Marginal cost & differential calculus
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Rates of change in other applied contexts (non-motion problems)Get 3 of 4 questions to level up!

Introduction to related rates

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Related rates intro
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Analyzing problems involving related rates
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Analyzing related rates problems: expressions
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Analyzing related rates problems: equations (Pythagoras)
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Analyzing related rates problems: equations (trig)
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Differentiating related functions intro
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Worked example: Differentiating related functions
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Practice
Analyzing related rates problems: expressionsGet 3 of 4 questions to level up!
Analyzing related rates problems: equationsGet 3 of 4 questions to level up!
Differentiate related functionsGet 3 of 4 questions to level up!

Solving related rates problems

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Related rates: Approaching cars
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Related rates: Falling ladder
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Related rates: water pouring into a cone
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Related rates: shadow
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Related rates: balloon
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Practice
Related rates introGet 3 of 4 questions to level up!
Related rates (multiple rates)Get 3 of 4 questions to level up!
Related rates (Pythagorean theorem)Get 3 of 4 questions to level up!
Related rates (advanced)Get 3 of 4 questions to level up!

Approximation with local linearity

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Local linearity
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Local linearity and differentiability
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Worked example: Approximation with local linearity
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Linear approximation of a rational function
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Practice
Approximation with local linearityGet 3 of 4 questions to level up!

L’Hôpital’s rule

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L'Hôpital's rule introduction
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L'Hôpital's rule: limit at 0 example
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L'Hôpital's rule: limit at infinity example
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L'Hôpital's rule: challenging problem
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L'Hôpital's rule: solve for a variable
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Proof of special case of l'Hôpital's rule
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Practice
L'Hôpital's rule: 0/0Get 3 of 4 questions to level up!
L'Hôpital's rule: ∞/∞Get 3 of 4 questions to level up!

L’Hôpital’s rule: composite exponential functions

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L’Hôpital’s rule (composite exponential functions)
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L'Hôpital's rule review
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L’Hôpital’s rule (composite exponential functions)Get 3 of 4 questions to level up!

About this unit

Derivatives describe the rate of change of quantities. This becomes very useful when solving various problems that are related to rates of change in applied, real-world, situations. Also learn how to apply derivatives to approximate function values and find limits using L’Hôpital’s rule.