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differentiation

The definition of the derivative

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Local knowledge map

Antiderivatives -- the reverse of differentiation Antiderivatives of trigonometric and exponential functions Backpropagation Basic antiderivative rules -- power, constant multiple,… Chain rule with exponential and logarithmic functions Chain rule with trigonometric functions Combining the chain rule with the product and quotient rules Differentials -- dy versus Delta y FTC Part 1 with variable limits of integration -- the… Higher-order derivatives Identifying composite-function structure for… Implicit differentiation L'Hopital's Rule: other indeterminate forms Local extrema and Fermat's theorem Newton's method for optimization Newton's method for root-finding, numerically Reading f' from the graph of f Sum and difference rules The generalized power rule The quotient rule The related-rates method U-substitution -- reversing the chain rule for indefinite… Constant, power, and constant-multiple rules Derivatives of trigonometric functions Differentiability and continuity L'Hopital's Rule: 0/0 and infinity/infinity Linear approximation Newton's method Rates of change in the sciences The chain rule The derivative as a function The product rule The definition of the derivative Continuity at a point Decompose composite functions Estimate limits numerically and graphically Limit laws Limits of complex functions Limits of sequences One-sided limits The Mean Value Theorem The precise (epsilon-delta) definition of a limit Trigonometric limits Velocity and acceleration Average vs. instantaneous rate of change What a limit means Difference quotient Instantaneous rate of change (limit intuition)

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