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# Advanced differentiation

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Implicit differentiationWorked example: Implicit differentiationWorked example: Evaluating derivative with implicit differentiationShowing explicit and implicit differentiation give same result

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Implicit differentiationGet 3 of 4 questions to level up!

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Implicit differentiation (advanced example)Implicit differentiation (advanced example)Implicit differentiation (advanced example)Derivative of ln(x) from derivative of 𝑒ˣ and implicit differentiationImplicit differentiation review

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Derivative of inverse sineDerivative of inverse cosineDerivative of inverse tangentDifferentiating inverse trig functions review

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Derivatives of inverse functions: from equationDerivatives of inverse functions: from table

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Derivatives of inverse functionsGet 3 of 4 questions to level up!

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Disguised derivatives

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Disguised derivativesGet 3 of 4 questions to level up!

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Proof: d/dx(ln x) = 1/xProof: d/dx(eˣ) = eˣProofs of derivatives of ln(x) and eˣ

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Composite exponential function differentiationWorked example: Composite exponential function differentiation

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Composite exponential function differentiationGet 3 of 4 questions to level up!

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Advanced differentiation challengeGet 3 of 4 questions to level up!

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Second derivativesSecond derivatives review

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Second derivativesGet 3 of 4 questions to level up!

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Mean value theoremMean value theorem example: polynomialMean value theorem example: square root functionMean value theorem applicationMean value theorem review

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