BackProduct and Quotient Rules definitions
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1/15BackSkip to main contentBackProduct Rule
A formula for finding the derivative of two multiplied functions, involving each function and the derivative of the other. Quotient Rule
A method for differentiating a function divided by another, using a specific formula involving subtraction and squaring the denominator. Derivative
A measure of how a function changes as its input changes, often representing instantaneous rate of change. Power Rule
A shortcut for differentiating terms with variables raised to powers, multiplying by the exponent and reducing it by one. Mnemonic Device
A memory aid, such as 'left d right plus right d left' or 'low d high minus high d low over the square of what's below,' for recalling rules. Numerator
The top part of a fraction, especially important in the setup of the quotient rule for derivatives. Denominator
The bottom part of a fraction, which is squared in the quotient rule when differentiating a quotient of functions. Simplification
The process of combining like terms and reducing expressions after applying differentiation rules. Like Terms
Terms in an expression that have identical variable parts and can be combined during simplification. Function
A mathematical relationship where each input has a single output, often represented as f(x) or g(x). Original Function
The unaltered part of a product or quotient before differentiation, used directly in both rules. Derivative Notation
Symbols such as f'(x), y', or ddx, indicating the derivative of a function. Polynomial
An expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication. Order of Operations
The sequence in which mathematical steps are performed, crucial when applying differentiation rules. Cancellation
The process of eliminating terms that offset each other, often occurring after applying the quotient rule.
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