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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 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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Chain rule with tablesGet 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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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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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!

About this unit

In Class XI, we had learnt to differentiate certain simple functions like polynomial functions and trigonometric functions. This year we'll pick up from there and learn new concepts of differentiability and continuity of functions.