RULES OF DERIVATIVES

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

Calculus is the mathematics of change, and the primary tool for studying change is a procedure called _______.

• Derivative

• Differentiable

• Differentiation

• Discontinuity

The derivative of a constant is

• two

• five

• one

• zero

Identify whether the following is differentiable and continuous: y=5x-1, x = 1

• continuous

• differentiable

• continuous and differentiable

• not continuous nor differentiable