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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 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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Disguised derivatives

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Proof: The derivative of 𝑒ˣ is 𝑒ˣProof: the derivative of ln(x) is 1/x

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Composite exponential function differentiationWorked example: Composite exponential function differentiation

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Vector-valued functions introVector-valued functions differentiationParametric equations differentiation

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Second derivativesSecond derivatives review

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Second derivatives (vector-valued functions)Second derivatives (parametric functions)

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