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3.2 Differentiation Chapter Contents
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Math 101 Chapter 3: Differentiation
Gordon Blower
3.2 Differentiation Chapter Contents
3.3 Instantaneous and average speed
3.4 Definition of the derivative
3.5 Differentiation from first principles
3.6 Leibniz’s rules for derivatives
3.7 Proof of Leibniz’s rules
3.8 Proof of Leibniz’s product rule.
3.9 Examples of Leibniz’s rules
3.10 Derivative formula by induction
3.11 Standard Derivatives
3.12 Derivatives examples
3.13 Derivative of the tangent function
3.14 Derivative of the exponential function
3.15 Derivatives of hyperbolic functions
3.16 Examples of rates of change
3.17 Growth and decay differential equation
3.18 Newton’s Law of Cooling
3.19 Solution of the cooling problem
3.20 Chain rule
3.21 Leibniz’s notation for chain rule
3.22 Examples of chain rule
3.23 Related rates of change
3.24 Inverse function rule
3.25 The derivative of
log
\log
3.26 Derivative of inverse cosine
3.27 Logarithmic differentiation
3.28 Differentiating powers
3.29 Equations of tangent and normal
3.30 Summary
3.31 Higher-order derivatives
3.32 Dynamical interpretation
3.33 Acceleration as the second derivative
3.34 Simple harmonic motion
3.35 Solution of simple harmonic motion
3.36 A differential equation for hyperbolic functions
3.37 Solution of differential equation for hyperbolic functions