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Implicit Differentiation definitions

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  • Implicit Differentiation
    A method for finding derivatives when a variable is embedded within an equation, not isolated on one side.
  • Chain Rule
    A technique for differentiating composite functions by multiplying the derivative of the outside by the derivative of the inside.
  • Power Rule
    A shortcut for differentiating expressions where a variable is raised to a constant exponent.
  • dy/dx
    A notation representing the derivative of one variable with respect to another, often appearing after implicit differentiation.
  • Algebraic Isolation
    A process of rearranging an equation to solve for a specific variable or expression, such as dy/dx.
  • Composite Function
    An expression where one function is nested inside another, requiring special rules for differentiation.
  • Constant
    A value in an equation that does not change and whose derivative with respect to any variable is zero.
  • Variable
    A symbol representing a quantity that can change, such as x or y, often differentiated in calculus.
  • Expression
    A combination of variables, constants, and operations forming a mathematical statement to be differentiated.
  • Square Root
    An operation that finds a value which, when multiplied by itself, gives the original number, often used to solve for y.
  • Equation
    A mathematical statement asserting the equality of two expressions, sometimes requiring implicit differentiation.
  • Derivative
    A measure of how a function changes as its input changes, central to calculus and implicit differentiation.
  • Outside Function
    The outermost operation in a composite function, differentiated first when applying the chain rule.
  • Inside Function
    The innermost operation in a composite function, whose derivative is multiplied when using the chain rule.