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Vectors and Derivatives (Product Rule): MATH 171 Problems 1-3 thumbnail

Vectors and Derivatives (Product Rule): MATH 171 Problems 1-3

Proving facts about the derivatives of vector functions including the product rule

CosineDerivativeDifference QuotientDot ProductGraphLimitLimit Definition of the DerivativeOrthogonalProduct RuleSineSum RuleTrigonometryVectorVector DerivativeVector Function
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Derivatives and Applications: MATH 171 Problems 7 & 8 thumbnail

Derivatives and Applications: MATH 171 Problems 7 & 8

Calculating slopes of tangent lines to parametric curves

CosineDerivativeLimitLimit from the LeftLimit from the RightLimit Involving InfinityParametric EquationsPerpendicularPolynomialProduct RuleSineTangent LineVectorVector Derivative
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Inverse Trigonometric Functions: MATH 171 Problems 4-6 thumbnail

Inverse Trigonometric Functions: MATH 171 Problems 4-6

Properties of inverse trig functions and the derivative of arctangent

AngleArccosineArcsineArctangentCodomainCosineDerivativeDifferentiationDomainGraphInverse FunctionInverse TrigonometryOne-to-oneSecantSineTangentTrigonometry
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Derivatives and Rates of Change: MATH 171 Problems 1-3 thumbnail

Derivatives and Rates of Change: MATH 171 Problems 1-3

Using the limit definition to find derivatives of functions and vector functions

DerivativeDifference QuotientGraphLimitLimit Definition of the DerivativeLineRational FunctionSlopeSquare RootTangent LineVectorVector DerivativeVector Function
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Differentiation Formulas: MATH 171 Problems 4 & 5 thumbnail

Differentiation Formulas: MATH 171 Problems 4 & 5

Using the limit definition to find a derivative and proving the power rule

Absolute ValueDerivativeDerivative RulesDifference QuotientLimit Definition of the DerivativePiecewise FunctionPower FunctionPower Rule
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Differentiation Formulas: MATH 171 Problems 6 & 7 thumbnail

Differentiation Formulas: MATH 171 Problems 6 & 7

Proving the Product Rule and the rule for the derivative of a difference of functions

Continuous FunctionDerivativeDerivative RulesDifference QuotientLimitLimit Definition of the DerivativeProduct Rule
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Differentials: MATH 171 Problems 1 & 2 thumbnail

Differentials: MATH 171 Problems 1 & 2

Proving facts about differentials including a product rule

DerivativeDifferentialLineLinear ApproximationProduct RuleTangent Line
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Higher Order Derivatives: MATH 171 Problems 4-6 thumbnail

Higher Order Derivatives: MATH 171 Problems 4-6

Finding a formula for a higher order derivative and a formula for the second derivative of a product

Chain RuleDerivativeFactorialHigher DerivativeInductionnth DerivativePower RuleProduct RuleRational FunctionSecond Derivative
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Trigonometry Derivatives and the Chain Rule: MATH 171 Problems 1-3 thumbnail

Trigonometry Derivatives and the Chain Rule: MATH 171 Problems 1-3

Proving the derivatives of trigonometric functions and that sine is continuous

ContinuousContinuous at x=aContinuous FunctionCosineDerivativeDifference QuotientLimitLimit Definition of the DerivativeQuotient RuleSecantSineTangentTrigonometry
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