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Differential Calculus: Math: Uncharted

Courses MathDifferential Calculus

Differential Calculus

The mathematics of change: limits, the derivative as a slope you can grab, the rules that compute it, and what it reveals about every curve.

Math
Unit 6 of 7
40 lessons
338 min
860 XP

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Lessons

40 total

1Closer and Closer, AgainDescribe a limit as the value a function approaches near an input.InteractiveConcept8 min20 XPOpen
2Read the LimitCompare graph values approaching the same input from the left and right.InteractiveConcept8 min20 XPOpen
3One Side at a TimeDecide whether matching one-sided limits create a two-sided limit.InteractiveConcept8 min20 XPOpen
4Limits by AlgebraFactor and cancel a removable factor to expose a limit.InteractiveConcept8 min20 XPOpen
5Limit WorkoutEvaluate factor-and-cancel limits at their approach points.InteractivePractice9 min20 XPOpen
6Off to InfinityRead the horizontal values rational functions settle toward.InteractiveConcept8 min20 XPOpen
7No Jumps AllowedDistinguish continuous points from removable holes and jumps.InteractiveConcept8 min20 XPOpen
8Limits Mastery CheckCombine algebraic, one-sided, and infinite limit readings.InteractiveMastery check9 min40 XPOpen
9Slope of a CurveUse shrinking secant intervals to approach a curve slope.InteractiveConcept8 min20 XPOpen
10Catch the TangentBuild the tangent line whose slope matches a curve at one point.InteractiveConcept8 min20 XPOpen
11The Derivative Is a FunctionRead derivative values as a new function of the input.InteractiveConcept8 min20 XPOpen
12The Power RuleSimplify a derivative produced by the power rule.InteractiveConcept8 min20 XPOpen
13Power Rule WorkoutDifferentiate drawn polynomials with the power rule.InteractivePractice9 min20 XPOpen
14The Product RuleSimplify the derivative created by differentiating a product.InteractiveConcept8 min20 XPOpen
15The Quotient RuleFactor the numerator produced by the quotient rule.InteractiveConcept8 min20 XPOpen
16The Chain RuleSimplify a derivative that combines outer and inner rates.InteractiveConcept8 min20 XPOpen
17Rules WorkoutDifferentiate mixed products, quotients, and compositions.InteractivePractice10 min20 XPOpen
18Trig and Exponential DerivativesDifferentiate sine, cosine, natural exponential, and logarithm terms.InteractiveConcept8 min20 XPOpen
19Implicit DifferentiationFind dy/dx when x and y are linked by one equation.InteractiveConcept8 min20 XPOpen
20Derivative DerivationsConnect raw rule applications to useful simplified derivatives.InteractivePractice10 min20 XPOpen
21Rules Mastery CheckSimplify a derivative that combines product and chain rules.InteractiveMastery check10 min40 XPOpen
22Up, Down, and FlatLocate points where a curve changes between increasing and decreasing.InteractiveConcept8 min20 XPOpen
23Find the Critical PointsSolve a factored derivative to locate critical inputs.InteractivePractice8 min20 XPOpen
24The Second DerivativeDifferentiate a polynomial twice and simplify the second derivative.InteractiveConcept8 min20 XPOpen
25Concave Which WayUse the sign of the second derivative to read concavity and inflection.InteractiveConcept8 min20 XPOpen
26Sketch from CluesPosition a curve sketch from values and derivative-sign clues.InteractiveConcept8 min20 XPOpen
27Motion on a LineDifferentiate position to obtain velocity and acceleration.InteractiveConcept8 min20 XPOpen
28Speeding Up or SlowingUse velocity and acceleration signs to decide whether speed grows.InteractiveConcept8 min20 XPOpen
29Behavior WorkoutConnect derivatives with critical points, concavity, and motion.InteractivePractice10 min20 XPOpen
30Read the RaceRecognize equal speeds from parallel position-graph segments.InteractiveConcept8 min20 XPOpen
31The Best BoxLocate the maximum of a volume function on its physical domain.InteractiveConcept8 min20 XPOpen
32Optimize ItMaximize a fenced area by solving where its derivative is zero.InteractivePractice8 min20 XPOpen
33The Sliding LadderRelate horizontal and vertical rates through a fixed-length constraint.InteractiveConcept8 min20 XPOpen
34Related Rates WorkoutCompute linked rates in geometric situations with drawn values.InteractivePractice10 min20 XPOpen
35The Tangent Lies WellUse a tangent line to estimate a nearby function value.InteractiveConcept8 min20 XPOpen
36Newton's ShortcutCompute one Newton-method step from a starting estimate.InteractiveConcept8 min20 XPOpen
37Applied WorkoutMix optimization, Newton steps, and tangent approximations.InteractivePractice10 min20 XPOpen
38Derivative of a StoryTranslate rate statements into derivative signs and magnitudes.InteractiveConcept8 min20 XPOpen
39Marginal ThinkingUse a cost derivative to estimate the next unit cost.InteractiveConcept8 min20 XPOpen
40Differential Calculus Mastery CheckSimplify a composite derivative and use it at a stated input.InteractiveMastery check11 min40 XPOpen

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