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The Chain Rule definitions

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  • Chain Rule
    A method for finding the derivative of a composite function by differentiating from the outermost function inward.
  • Composite Function
    An expression formed by applying one function to the result of another, often written as f(g(x)).
  • Outside Function
    The function applied last in a composite, differentiated first when using the chain rule.
  • Inside Function
    The function nested within another, treated as a variable when differentiating the outside function.
  • Power Rule
    A shortcut for differentiating expressions with exponents by multiplying by the exponent and reducing it by one.
  • Leibnitz Notation
    A symbolic way to express derivatives, such as dydx = dydu * dudx, useful for the chain rule.
  • Parentheses
    A notation often used to visually group the inside function within a composite expression.
  • Simplification
    The process of combining like terms or constants after differentiation to present the derivative in its cleanest form.
  • Trig Function
    A function like sine or cosine, which may be raised to a power and require rewriting for easier differentiation.
  • Variable
    A symbol, often x, treated as a placeholder when differentiating composite functions.
  • Exponent
    A number indicating how many times a base is multiplied by itself, crucial in applying the power rule.
  • Derivative
    A measure of how a function changes as its input changes, found using rules like the chain rule.
  • Notation
    A system of symbols used to represent mathematical ideas, such as derivatives and composite functions.
  • Sine Function
    A trigonometric function often appearing in composite forms, requiring careful application of the chain rule.
  • Cosine Function
    The derivative of the sine function, frequently encountered when differentiating trigonometric composites.