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๐Ÿ“˜ Techniques of Derivatives

The differentiation toolkit: the rules that turn $f(x)$ into $f'(x)$ for every shape of function you'll meet โ€” products, quotients, composites, exponentials, logarithms, and implicitly-defined curves.

Topics

๐Ÿ“‹ Introduction (Pretest)

Diagnostic: see what you remember and what needs work.

Coming when we start

๐Ÿ“ Power Rule and Constant Rule

The workhorses โ€” differentiate $x^n$ and constants.

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โœ–๏ธ Product Rule

$(fg)' = f'g + fg'$.

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โž— Quotient Rule

$(f/g)' = \frac{f'g - fg'}{g^2}$.

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๐Ÿ”— Chain Rule

Composite functions โ€” the rule that makes calc II work.

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๐Ÿ“ˆ Derivatives of Exponential and Logarithmic Functions

$e^x$, $a^x$, $\ln x$, $\log_a x$.

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๐Ÿ”„ Implicit Differentiation

Differentiate equations like $x^2 + y^2 = 1$ without solving for $y$.

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โœ… Conclusion (Posttest)

End-of-module assessment.

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