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Basic differentiation rules

Learn
Basic derivative rules (Part 1)
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Basic derivative rules (Part 2)
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Basic derivative rules: find the error
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Basic derivative rules: table
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Basic differentiation review
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Practice
Basic derivative rules: find the errorGet 3 of 4 questions to level up!
Basic derivative rules: tableGet 3 of 4 questions to level up!

Power rule

Learn
Power rule
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Justifying the power rule
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Practice
Power rule (positive integer powers)Get 3 of 4 questions to level up!

Polynomial functions differentiation

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Basic derivative rules
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Differentiating polynomials
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Tangents of polynomials
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Differentiating polynomials review
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Practice
Differentiate polynomialsGet 3 of 4 questions to level up!
Tangents of polynomialsGet 3 of 4 questions to level up!

Quiz 1

Level up on the above skills and collect up to 500 Mastery points

Derivatives of negative and fractional powers with power rule

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Differentiating integer powers (mixed positive and negative)
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Fractional powers differentiation
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Radical functions differentiation intro
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Worked example: Tangent to the graph of 1/x
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Power rule review
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Practice
Power rule (negative & fractional powers)Get 3 of 4 questions to level up!
Power rule (with rewriting the expression)Get 3 of 4 questions to level up!
Differentiate integer powers (mixed positive and negative)Get 3 of 4 questions to level up!

Derivatives of sin(x) and cos(x)

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Derivatives of sin(x) and cos(x)
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Worked example: Derivatives of sin(x) and cos(x)
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Proving the derivatives of sin(x) and cos(x)
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Practice
Derivatives of sin(x) and cos(x)Get 3 of 4 questions to level up!

Quiz 2

Level up on the above skills and collect up to 400 Mastery points

Product rule

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Product rule
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Differentiating products
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Worked example: Product rule with table
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Worked example: Product rule with mixed implicit & explicit
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Proving the product rule
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Product rule review
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Practice
Differentiate productsGet 3 of 4 questions to level up!
Product rule with tablesGet 3 of 4 questions to level up!

Quotient rule

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Quotient rule
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Worked example: Quotient rule with table
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Quotient rule review
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Practice
Differentiate quotientsGet 3 of 4 questions to level up!
Quotient rule with tablesGet 3 of 4 questions to level up!

Rational functions differentiation

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Differentiating rational functions
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Linear approximation of a rational function
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Differentiating rational functions review
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Practice
Differentiate rational functionsGet 3 of 4 questions to level up!

Quiz 3

Level up on the above skills and collect up to 500 Mastery points

Chain rule

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Chain rule
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Chain rule
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Identifying composite functions
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Worked example: Derivative of cos³(x) using the chain rule
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Worked example: Derivative of √(3x²-x) using the chain rule
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Common chain rule misunderstandings
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Worked example: Chain rule with table
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Proving the chain rule
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Practice
Identify composite functionsGet 3 of 4 questions to level up!
Chain rule introGet 3 of 4 questions to level up!
Chain rule with tablesGet 3 of 4 questions to level up!

Radical functions differentiation

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Worked example: Derivative of ∜(x³+4x²+7) using the chain rule
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Practice
Differentiate radical functionsGet 3 of 4 questions to level up!

Trigonometric functions differentiation

Learn
Derivatives of tan(x) and cot(x)
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Derivatives of sec(x) and csc(x)
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Worked example: Derivative of sec(3π/2-x) using the chain rule
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Differentiating trigonometric functions review
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Practice
Derivatives of tan(x), cot(x), sec(x), and csc(x)Get 5 of 7 questions to level up!
Differentiate trigonometric functionsGet 3 of 4 questions to level up!

Strategy in differentiating functions

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Differentiating functions: Find the error
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Manipulating functions before differentiation
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Strategy in differentiating functions
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Derivative rules review
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Practice
Differentiating functions: Find the errorGet 3 of 4 questions to level up!
Manipulating functions before differentiationGet 3 of 4 questions to level up!

Quiz 4

Level up on the above skills and collect up to 800 Mastery points

Optional videos

Learn
Justifying the power rule
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Proof of power rule for positive integer powers
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Proof of power rule for square root function
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Limit of sin(x)/x as x approaches 0
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Limit of (1-cos(x))/x as x approaches 0
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Proof of the derivative of sin(x)
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Proof of the derivative of cos(x)
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Product rule proof
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Proof: Differentiability implies continuity
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If function u is continuous at x, then Δu→0 as Δx→0
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Chain rule proof
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Quotient rule from product & chain rules
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Unit test

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About this unit

The definition for the derivative of a function is very important, but it isn't the fastest way for actually finding the derivative of various functions. In this unit we will learn the main rules in which we can apply to quickly find the derivatives of common functions.