constant multiple rule
[constant multiple rule|constant multiple rule] The constant multiple rule is applied when differentiating a term with a constant factor.
Mechanism
constant multiple rule The constant multiple rule is applied when differentiating a term with a constant factor. It simplifies the differentiation process by allowing the constant to be factored out, as demonstrated in the example where 2x5 is differentiated to 10x.
Comparison
constant multiple rule Applying the constant multiple rule, the derivative of g(x) = 3x² is calculated by multiplying the constant 3 with the derivative of x², resulting in 6x. This solution directly compares to the derivative of f(x) = x², which is 2x, demonstrating how the rule scales the rate of change by the constant factor.
Examples
constant multiple rule Apply the constant multiple rule to differentiate 3(x) and the product rule to differentiate x7 g(x). Example 3.29 Extending the Product Rule For k(x) = f)g(x)h(x), express k'(x) in terms of f(x), g(x), A(x), and their derivatives.