Rules of differentiation

This rule states that the derivative of a constant function is zero; that is, since a constant function is a horizontal line, the slope, or the rate of change, of a constant function is 0.

• The Power Rule

• The Constant Rule

• The Sum, Difference, and Constant Multiple Rules

• The Product Rule

This rule is used to differentiate functions of the form f(x) = x^r, whenever r is a real number.

• The Sum, Difference, and Constant Multiple Rules

• The Product Rule

• The Quotient Rule

• The Power Rule

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.

• Sum Rule

• Difference Rule

• Constant Multiple Rule

• The Sum, Difference, and Constant Multiple Rules

The derivative of a constant k multiplied by a function f is the same as the constant multiplied by the derivative.

• Constant Multiple Rule

• The Sum, Difference, and Constant Multiple Rules

• Difference Rule

• Sum Rule

The derivative of the difference of a function f and a function g is the same as the difference of the derivative of f and the derivative of g.

• Sum Rule

• The Sum, Difference, and Constant Multiple Rules

• Difference Rule

• Constant Multiple Rule

This rule says that the derivative of a product of two functions is the first function times the derivative of the second function plus the second function times the derivative of the first function.

• The Product Rule

• Constant Multiple Rule

• The Power Rule

• The Constant Rule

This rule states that the derivative of a quotient is the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by the square of the denominator.

• The Sum, Difference, and Constant Multiple Rules

• The Power Rule

• Constant Multiple Rule

• The Quotient Rule

The functions f (x) = c and g (x) = x n where n is a _____ are the building blocks from which all polynomials and rational functions are constructed.

To find derivatives of polynomials and rational functions efficiently without resorting to the limit definition of the derivative, we must first develop _____ for differentiating these basic functions.

The basic _______ allow us to compute the derivatives of such functions without using the formal definition of the derivative.