Differential Calculus
Explore the definition of derivatives and master basic calculation rules, building foundational skills in differential calculus to analyze and interpret mathematical changes effectively.
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VIDEOS
Newton, Leibniz, and Usain Bolt
Khan Academy
•9th - 12th Grade
•10 Qs
Secant lines & average rate of change
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•9th - 12th Grade
•10 Qs
Derivative as a concept
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•9th - 12th Grade
•10 Qs
The derivative & tangent line equations
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•9th - 12th Grade
•10 Qs
Derivative as slope of curve
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•6th - 10th Grade
•10 Qs
VIDEOS
Secant line with arbitrary point
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•9th - 12th Grade
•10 Qs
Slope of a line secant to a curve
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•8th - 12th Grade
•10 Qs
Secant line with arbitrary difference
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•10th - 12th Grade
•10 Qs
Secant line with arbitrary difference (with simplification)
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•9th - 12th Grade
•10 Qs
Secant line with arbitrary point (with simplification)
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•9th - 12th Grade
•10 Qs
Secant lines: challenging problem 1
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•9th - 12th Grade
•10 Qs
Secant lines: challenging problem 2
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•10th - 12th Grade
•10 Qs
VIDEOS
Formal definition of the derivative as a limit
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•1th - 13th Grade
•10 Qs
Worked example: Derivative as a limit
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•10th - 12th Grade
•10 Qs
Formal and alternate form of the derivative
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•9th - 12th Grade
•10 Qs
The derivative of x² at x=3 using the formal definition
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•9th - 12th Grade
•10 Qs
The derivative of x² at any point using the formal definition
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•9th - 12th Grade
•10 Qs
Worked example: Derivative from limit expression
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•9th - 12th Grade
•10 Qs
Limit expression for the derivative of function (graphical)
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•10th - 12th Grade
•10 Qs
VIDEOS
Differentiability and continuity
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•11th - 13th Grade
•10 Qs
Differentiability at a point: algebraic (function is differentiable)
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•9th - 12th Grade
•10 Qs
Differentiability at a point: graphical
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•9th - 12th Grade
•10 Qs
Differentiability at a point: algebraic (function isn't differentiable)
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•9th - 12th Grade
•10 Qs
VIDEOS
VIDEOS
VIDEOS
Worked example: Quotient rule with table
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•10th - 12th Grade
•10 Qs
Quotient rule
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•9th - 12th Grade
•10 Qs
Tangent to y=𝑒ˣ/(2+x³)
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•10th - 12th Grade
•10 Qs
Differentiating rational functions
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•9th - 12th Grade
•10 Qs
Normal to y=𝑒ˣ/x²
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•10th - 12th Grade
•10 Qs
VIDEOS
Proof: Differentiability implies continuity
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•11th - 13th Grade
•10 Qs
Proof of power rule for positive integer powers
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•9th - 12th Grade
•10 Qs
Justifying the power rule
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•9th - 12th Grade
•10 Qs
Proof of power rule for square root function
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•9th - 12th Grade
•10 Qs
Limit of sin(x)/x as x approaches 0
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•11th - 13th Grade
•10 Qs
Limit of (1-cos(x))/x as x approaches 0
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•9th - 12th Grade
•10 Qs
Proof of the derivative of sin(x)
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•10th - 12th Grade
•10 Qs
Proof of the derivative of cos(x)
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•9th - 12th Grade
•10 Qs
Product rule proof
Khan Academy
•10th - 12th Grade
•10 Qs