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Unit: Advanced derivatives

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Differentiating using multiple rules

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Differentiating using multiple rules: strategy
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Applying the chain rule and product rule
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Applying the chain rule twice
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Practice
Differentiating using multiple rules: strategyGet 3 of 4 questions to level up!
Differentiating using multiple rulesGet 3 of 4 questions to level up!

Second derivatives

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Second derivatives
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Second derivatives review
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Second derivativesGet 3 of 4 questions to level up!

Quiz 1

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Implicit differentiation

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Implicit differentiation
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Worked example: Implicit differentiation
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Worked example: Evaluating derivative with implicit differentiation
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Differentiating related functions intro
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Worked example: Differentiating related functions
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Showing explicit and implicit differentiation give same result
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Implicit differentiation review
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Practice
Implicit differentiationGet 3 of 4 questions to level up!
Differentiate related functionsGet 3 of 4 questions to level up!

Derivatives of inverse functions

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Derivatives of inverse functions
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Derivatives of inverse functions: from equation
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Derivatives of inverse functions: from table
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Derivatives of inverse functionsGet 3 of 4 questions to level up!

Quiz 2

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Derivatives of inverse trigonometric functions

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Derivative of inverse sine
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Derivative of inverse cosine
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Derivative of inverse tangent
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Differentiating inverse trig functions review
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Practice
Derivatives of inverse trigonometric functionsGet 3 of 4 questions to level up!

Derivatives of exponential functions

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𝑒 and compound interest
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𝑒 as a limit
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Derivative of 𝑒ˣ
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Derivative of aˣ (for any positive base a)
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Worked example: Derivative of 7^(x²-x) using the chain rule
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Differentiating exponential functions review
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Proof: The derivative of 𝑒ˣ is 𝑒ˣ
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Derivative of eᶜᵒˢˣ⋅cos(eˣ)
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Practice
Derivatives of aˣ and logₐxGet 3 of 4 questions to level up!
Differentiate exponential functionsGet 3 of 4 questions to level up!

Derivatives of logarithmic functions

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Derivative of ln(x)
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Derivative of logₐx (for any positive base a≠1)
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Worked example: Derivative of log₄(x²+x) using the chain rule
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Differentiating logarithmic functions review
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Common derivatives review
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Proof: the derivative of ln(x) is 1/x
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Worked example: Derivative of ln(√x) using the chain rule
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Derivative of sin(ln(x²))
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Differentiating logarithmic functions using log properties
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Practice
Differentiate logarithmic functionsGet 3 of 4 questions to level up!

Quiz 3

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Optional videos

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Proof: The derivative of 𝑒ˣ is 𝑒ˣ
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Proof: the derivative of ln(x) is 1/x
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Derivative of ln(x) from derivative of 𝑒ˣ and implicit differentiation
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Unit test

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About this unit

This unit covers cases where we apply the common derivative rules in more elaborate ways. For example, implicit differentiation uses the chain rule to find the derivatives of functions whose explicit equation is unknown.