29 lines
653 B
Markdown
29 lines
653 B
Markdown
---
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id: mat-02-derivatives
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title: "Derivatives: definition and rules"
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---
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# Derivatives
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## Derivative definition
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The derivative at a point is the limit of the difference quotient.
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## Derivative rules
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Key rules include:
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- constant and power rule
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- sum and product rule
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- quotient rule
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- chain rule
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## Derivatives of common functions
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Examples:
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- derivative of x^n
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- derivative of sin x and cos x
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- derivative of e^x and ln x
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## Tangent line approximation
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A derivative gives the slope of the tangent line and supports local linear approximation.
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## Critical points
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Critical points occur where the derivative is zero or undefined (within the domain).
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