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- https://math.libretexts.org/Courses/Chabot_College/MTH_1%3A_Calculus_I/03%3A_Derivatives/3.02%3A_Differentiation_RulesThe derivative of a constant function is zero. The derivative of a power function is a function in which the power on x becomes the coefficient of the term and the power on x in the derivative decrea...The derivative of a constant function is zero. The derivative of a power function is a function in which the power on x becomes the coefficient of the term and the power on x in the derivative decreases by 1. The derivative of a constant c multiplied by a function f is the same as the constant multiplied by the derivative. The derivative of the sum of a function f and a function g is the same as the sum of the derivative of f and the derivative of g.
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_400%3A_Calculus_I_-_Differential_Calculus/03%3A_Discovering_Derivatives/3.01%3A_Derivatives_of_Polynomial_FunctionsThis section covers how to find the derivatives of polynomial functions. It introduces the basic power rule for differentiation and demonstrates how to apply it to terms of various degrees. The sectio...This section covers how to find the derivatives of polynomial functions. It introduces the basic power rule for differentiation and demonstrates how to apply it to terms of various degrees. The section includes examples of differentiating polynomials and highlights the key steps for finding first and higher-order derivatives of polynomial functions. The focus is on understanding the straightforward process of differentiating terms of the form xn.
- https://math.libretexts.org/Courses/Laney_College/Math_3A%3A_Calculus_1_(Fall_2022)/03%3A_Derivatives/3.04%3A_Differentiation_RulesThe derivative of a constant function is zero. The derivative of a power function is a function in which the power on x becomes the coefficient of the term and the power on x in the derivative decrea...The derivative of a constant function is zero. The derivative of a power function is a function in which the power on x becomes the coefficient of the term and the power on x in the derivative decreases by 1. The derivative of a constant c multiplied by a function f is the same as the constant multiplied by the derivative. The derivative of the sum of a function f and a function g is the same as the sum of the derivative of f and the derivative of g.
- https://math.libretexts.org/Courses/Penn_State_University_Greater_Allegheny/Math_140%3A_Calculus_1_(Gaydos)/03%3A_Derivatives/3.03%3A_Differentiation_RulesThe derivative of a constant function is zero. The derivative of a power function is a function in which the power on x becomes the coefficient of the term and the power on x in the derivative decrea...The derivative of a constant function is zero. The derivative of a power function is a function in which the power on x becomes the coefficient of the term and the power on x in the derivative decreases by 1. The derivative of a constant c multiplied by a function f is the same as the constant multiplied by the derivative. The derivative of the sum of a function f and a function g is the same as the sum of the derivative of f and the derivative of g.
- https://math.libretexts.org/Under_Construction/Purgatory/Remixer_University/Username%3A_hdagnew@ucdavis.edu/Courses%2F%2FRemixer_University%2F%2FUsername%3A_hdagnew@ucdavis.edu%2F%2FMonroe2/Courses%2F%2FRemixer_University%2F%2FUsername%3A_hdagnew@ucdavis.edu%2F%2FMonroe2%2F%2FChapter_3%3A_Derivatives/Courses%2F%2FRemixer_University%2F%2FUsername%3A_hdagnew@ucdavis.edu%2F%2FMonroe2%2F%2FChapter_3%3A_Derivatives%2F%2F3.3%3A_(and_3.4)_Differentiation_RulesAs we see in the following theorem, the derivative of the quotient is not the quotient of the derivatives; rather, it is the derivative of the function in the numerator times the function in the denom...As we see in the following theorem, the derivative of the quotient is not the quotient of the derivatives; rather, it is the derivative of the function in the numerator times the function in the denominator minus the derivative of the function in the denominator times the function in the numerator, all divided by the square of the function in the denominator.
- https://math.libretexts.org/Courses/Monroe_Community_College/MTH_210_Calculus_I_(Professor_Dean)/professor_playground/3.4%3A_Product_and_Quotient_RulesAs we see in the following theorem, the derivative of the quotient is not the quotient of the derivatives; rather, it is the derivative of the function in the numerator times the function in the denom...As we see in the following theorem, the derivative of the quotient is not the quotient of the derivatives; rather, it is the derivative of the function in the numerator times the function in the denominator minus the derivative of the function in the denominator times the function in the numerator, all divided by the square of the function in the denominator.
- https://math.libretexts.org/Courses/Borough_of_Manhattan_Community_College/MAT301_Calculus_I/03%3A_Derivatives/3.04%3A_(and_3.4)_Differentiation_RulesAs we see in the following theorem, the derivative of the quotient is not the quotient of the derivatives; rather, it is the derivative of the function in the numerator times the function in the denom...As we see in the following theorem, the derivative of the quotient is not the quotient of the derivatives; rather, it is the derivative of the function in the numerator times the function in the denominator minus the derivative of the function in the denominator times the function in the numerator, all divided by the square of the function in the denominator.
- https://math.libretexts.org/Courses/Borough_of_Manhattan_Community_College/MAT301_Calculus_I/06%3A_professor_playground/6.04%3A_Product_and_Quotient_RulesAs we see in the following theorem, the derivative of the quotient is not the quotient of the derivatives; rather, it is the derivative of the function in the numerator times the function in the denom...As we see in the following theorem, the derivative of the quotient is not the quotient of the derivatives; rather, it is the derivative of the function in the numerator times the function in the denominator minus the derivative of the function in the denominator times the function in the numerator, all divided by the square of the function in the denominator.
- https://math.libretexts.org/Courses/City_College_of_San_Francisco/CCSF_Calculus/03%3A_Discovering_Derivatives/3.02%3A_Differentiation_Techniques_-_The_Product_and_Quotient_RulesThis section introduces the Product and Quotient Rules for differentiation. It explains how to differentiate products of two functions using the Product Rule and quotients using the Quotient Rule. Exa...This section introduces the Product and Quotient Rules for differentiation. It explains how to differentiate products of two functions using the Product Rule and quotients using the Quotient Rule. Examples demonstrate the step-by-step process for applying these rules to various functions, helping to differentiate more complex expressions involving multiplication and division of functions.
- https://math.libretexts.org/Bookshelves/Calculus/Calculus_3e_(Apex)/05%3A_Integration/5.01%3A_Antiderivatives_and_Indefinite_IntegrationThis section introduced antiderivatives and the indefinite integral. We found they are needed when finding a function given information about its derivative(s). There are numerous reasons this will pr...This section introduced antiderivatives and the indefinite integral. We found they are needed when finding a function given information about its derivative(s). There are numerous reasons this will prove to be useful: these functions will help us compute areas, volumes, mass, force, pressure, work, and much more.
- https://math.libretexts.org/Courses/Lake_Tahoe_Community_College/Interactive_Calculus_Q1/03%3A_Derivatives/3.04%3A_Differentiation_RulesThe derivative of a constant function is zero. The derivative of a power function is a function in which the power on x becomes the coefficient of the term and the power on x in the derivative decrea...The derivative of a constant function is zero. The derivative of a power function is a function in which the power on x becomes the coefficient of the term and the power on x in the derivative decreases by 1. The derivative of a constant c multiplied by a function f is the same as the constant multiplied by the derivative. The derivative of the sum of a function f and a function g is the same as the sum of the derivative of f and the derivative of g.
