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Basic Rules of Differentiation definitions

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  • Derivative
    Slope of the tangent line to a function, representing the instantaneous rate of change at any point.
  • Constant Function
    A function whose graph is a horizontal line, always yielding a zero slope for its tangent.
  • Power Rule
    A shortcut for finding the derivative of any power function by multiplying by the exponent and reducing it by one.
  • Sum Rule
    A method allowing the derivative of a sum to be found by adding the derivatives of each term separately.
  • Difference Rule
    A method allowing the derivative of a difference to be found by subtracting the derivatives of each term.
  • Constant Multiple Rule
    A rule that allows constants to be factored out before differentiating the remaining function.
  • Linear Function
    A function whose graph is a straight line, with a constant rate of change at every point.
  • Exponent
    A value indicating how many times a base is used as a factor, crucial in applying the power rule.
  • Negative Exponent
    An exponent indicating reciprocal powers, which can be handled by rewriting before differentiation.
  • Rational Exponent
    An exponent expressed as a fraction, allowing roots to be rewritten as powers for easier differentiation.
  • Tangent Line
    A straight line touching a curve at a single point, sharing the same instantaneous slope as the curve there.
  • Slope
    A measure of steepness, given by the derivative at a specific point on a function.
  • Power Function
    A function of the form x raised to any real exponent, suitable for direct application of the power rule.
  • Cube Root
    A value that, when raised to the third power, yields the original number; can be rewritten as a rational exponent.
  • Reciprocal Function
    A function of the form 1/x, which can be rewritten with a negative exponent for differentiation.