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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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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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Exponentials and Hyperbolic Trigonometric Functions: MATH 171 Problems 3 & 4 thumbnail

Exponentials and Hyperbolic Trigonometric Functions: MATH 171 Problems 3 & 4

Examples involving the tangent line to an exponential function and finding the derivative of hyperbolic cosine

Chain RuleCosineDerivativeExponential FunctionHyperbolic CosineHyperbolic FunctionsHyperbolic SineHyperbolic TrigonometryLineSineTangent Linex-Intercept
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Derivatives of Logarithmic Functions: MATH 171 Problems 7-9 thumbnail

Derivatives of Logarithmic Functions: MATH 171 Problems 7-9

Proving facts about logarithms and exponentials including the derivative of an exponential with an arbitrary base

Chain RuleeEpsilon-Delta Definition of a LimitExponential FunctionInverse FunctionLimitLimit Involving InfinityLogarithmLogarithm Properties
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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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L'Hospital's Rule: MATH 171 Problems 7-9 thumbnail

L'Hospital's Rule: MATH 171 Problems 7-9

Proving L'Hospital's Rule and using it to evaluate limits

Chain RuleContinuousContinuous at x=aDerivativeDifferentiableeGraphIndeterminate FormL'Hopital's RuleLimitLimit Involving InfinityLogarithm
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Higher Derivatives Example 2 thumbnail

Higher Derivatives Example 2

Using derivatives to find the velocity and acceleration functions from the position function

AccelerationChain RuleDerivativeFirst DerivativeHigher DerivativeMATH 147PositionPower FunctionPower RuleSecond DerivativeSquare RootVelocity
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Derivatives of Exponential Functions thumbnail

Derivatives of Exponential Functions

Explaining the formulas for the derivatives of exponential functions

Chain RuleDerivativeExponential FunctionLimitLogarithmLogarithm PropertiesMATH 147Power Rule
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