Generalized Powers: Derivatives and Exponentials

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Introduces derivatives, trigonometry, and motion principles through basic and trigonometric functions differentiation.

Explores the properties and graph of the natural logarithm function, emphasizing its bijectivity and the Euler's number 'e'.

Explores the properties and applications of natural logarithmic functions, including area invariance and harmonic series divergence.

Explores the definition and properties of derivatives, including slopes of tangent lines and differentiability conditions.

Covers the rules of derivatives, O-notation, and extrema in the context of theorem 6.5 and examples.

Covers partial derivatives for functions of one and two variables, emphasizing their importance and calculation.

Covers algebraic identities, trigonometry, and real functions, including injective, surjective, bijective, and reciprocal functions.

Explores exponential and logarithmic functions, their properties, relations, and graphs, including different bases and commonly used logarithms.

Provides solutions to an Analysis I exam, covering various topics.

Explores differentiability in two variables and the chain rule for compositions.