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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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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 2: MATH 171 Problems 4 & 5 thumbnail

Trigonometry Derivatives and the Chain Rule 2: MATH 171 Problems 4 & 5

Using the Chain Rule to prove facts about derivatives

Chain RuleDerivativeDifferentiableEven FunctionFactoringOdd FunctionPolynomialProduct Rule
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Derivatives of Logarithmic Functions: MATH 171 Problems 1-3 thumbnail

Derivatives of Logarithmic Functions: MATH 171 Problems 1-3

Proving the derivative of ln(x) and the power and product rules using logarithmic differentiation

Chain RuleDerivativeDifferentiableDifferentiationeImplicit DifferentiationLogarithmLogarithmic DifferentiationPower FunctionPower RuleProduct Rule
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Derivatives of Exponential Functions Example 1 thumbnail

Derivatives of Exponential Functions Example 1

Calculating the derivative of a function with exponentials using the chain and product rule

Chain RuleDerivativeExponential FunctionMATH 147PolynomialPower RuleProduct Rule
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Integration by Parts: MATH 172 Problems 1 & 2 thumbnail

Integration by Parts: MATH 172 Problems 1 & 2

Proving the formula for integration by parts and a reduction formula

DerivativeFundamental Theorem of CalculusIndefinite IntegralIntegral RulesIntegration by PartsProduct RuleSecant
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