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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)

About this unit

The chain rule sets the stage for implicit differentiation, which in turn allows us to differentiate inverse functions (and specifically the inverse trigonometric functions). This is really the top of the line when it comes to differentiation.