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# Continuity & differentiability

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Continuity introductionWorked example: Continuity at a point (graphical)

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Continuity at a point (graphical)Get 3 of 4 questions to level up!

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Limit propertiesLimits of combined functionsLimits of composite functions

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Limits of combined functions: products and quotientsGet 3 of 4 questions to level up!

Limits of composite functionsGet 3 of 4 questions to level up!

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Functions continuous on all real numbersFunctions continuous at specific x-values

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Continuity and common functionsGet 3 of 4 questions to level up!

Continuity challengeGet 5 of 7 questions to level up!

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Intermediate value theoremWorked example: using the intermediate value theoremIntermediate value theorem review

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Using the intermediate value theoremGet 3 of 4 questions to level up!

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Differentiability at a point: graphicalDifferentiability at a point: algebraic (function is differentiable)Differentiability at a point: algebraic (function isn't differentiable)

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Differentiability at a point: graphicalGet 3 of 4 questions to level up!

Differentiability at a point: algebraicGet 3 of 4 questions to level up!

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Derivatives basics challengeGet 5 of 7 questions to level up!

Basic differentiation challengeGet 5 of 7 questions to level up!

Power rule challengeGet 5 of 7 questions to level up!

Common derivatives challengeGet 5 of 7 questions to level up!

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Product ruleDifferentiating productsWorked example: Product rule with tableWorked example: Product rule with mixed implicit & explicitProduct rule to find derivative of product of three functionsProduct rule proofProduct rule review

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Differentiate productsGet 3 of 4 questions to level up!

Product rule with tablesGet 3 of 4 questions to level up!

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Quotient rule from product & chain rulesWorked example: Quotient rule with tableTangent to y=𝑒ˣ/(2+x³)Normal to y=𝑒ˣ/x²Quotient rule review

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Differentiate quotientsGet 3 of 4 questions to level up!

Quotient rule with tablesGet 3 of 4 questions to level up!

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Chain ruleWorked example: Derivative of cos³(x) using the chain ruleWorked example: Derivative of ln(√x) using the chain ruleWorked example: Derivative of √(3x²-x) using the chain ruleChain rule overviewWorked example: Chain rule with tableChain rule

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Differentiate composite functions (all function types)Get 3 of 4 questions to level up!

Chain rule with tablesGet 3 of 4 questions to level up!

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Product, quotient, & chain rules challengeGet 3 of 4 questions to level up!

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Differentiating rational functionsDifferentiating rational functions review

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Differentiate rational functionsGet 3 of 4 questions to level up!

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Worked example: Derivative of ∜(x³+4x²+7) using the chain rule

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Differentiate radical functionsGet 3 of 4 questions to level up!

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Derivatives of tan(x) and cot(x)Derivatives of sec(x) and csc(x)Worked example: Derivative of sec(3π/2-x) using the chain ruleDifferentiating trigonometric functions review

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Derivatives of tan(x), cot(x), sec(x), and csc(x)Get 5 of 7 questions to level up!

Differentiate trigonometric functionsGet 3 of 4 questions to level up!

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Derivatives of sin(x), cos(x), tan(x), eˣ & ln(x)Derivative of aˣ (for any positive base a)Worked example: Derivative of 7^(x²-x) using the chain ruleDifferentiating exponential functions review

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Derivatives of aˣ and logₐxGet 3 of 4 questions to level up!

Differentiate exponential functionsGet 3 of 4 questions to level up!

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Derivative of logₐx (for any positive base a≠1)Worked example: Derivative of log₄(x²+x) using the chain ruleDifferentiating logarithmic functions using log propertiesDifferentiating logarithmic functions review

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Logarithmic functions differentiation introGet 3 of 4 questions to level up!

Differentiate logarithmic functionsGet 3 of 4 questions to level up!

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Derivative of eᶜᵒˢˣ⋅cos(eˣ)Derivative of sin(ln(x²))Common derivatives reviewDerivative rules review

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Differentiating using multiple rulesGet 3 of 4 questions to level up!

Tangents & normal lines challengeGet 3 of 4 questions to level up!