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Differentials definitions

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  • Derivative
    Slope of the tangent line to a function at a point, representing the rate of change with respect to the independent variable.
  • Differential
    Small change in a function's output, estimated by multiplying the derivative by a small change in the input.
  • dx
    Infinitesimal change in the independent variable, used to approximate small variations in function values.
  • dy
    Approximate change in the dependent variable, calculated as the derivative times dx for small input changes.
  • Power Rule
    Shortcut for finding the derivative of a term with a variable raised to a power, multiplying by the exponent and reducing it by one.
  • Tangent Line
    Straight line that touches a curve at a single point, sharing the same slope as the curve at that point.
  • Approximate Value
    Estimated result for a function, often found using differentials when exact calculation is difficult.
  • Exact Value
    True result of a function, obtained by direct calculation without estimation or rounding.
  • Absolute Error
    Non-negative difference between the exact value and the approximate value, indicating the size of the estimation mistake.
  • Relative Error
    Ratio of absolute error to the exact value, providing a sense of the error's size compared to the true result.
  • Percentage Error
    Relative error expressed as a percent, showing how far off an approximation is in terms of the exact value.
  • Delta x
    Finite change in the independent variable, often compared to dx for small increments in calculus.
  • Delta y
    Finite change in the dependent variable, closely related to dy for small changes in input.
  • Slope
    Measure of steepness of a line, given by the ratio of vertical change to horizontal change between two points.
  • Function
    Mathematical relationship assigning each input exactly one output, often written as y = f(x).