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Match the rule with the title. \frac{\mathrm{d} }{\mathrm{d} x} \left [cf(x)\right ]= cf'(x) A....

Question:

Match the rule with the title.

{eq}\frac{\mathrm{d} }{\mathrm{d} x} \left [cf(x)\right ]= cf'(x) {/eq}

A. Constant Rule

B. Single Variable Rule

C. Power Rule

D. Constant Multiple Rule.

E. Sum and Difference Rule

F. Product Rule

G. Quotient Rule

H. Chain Rule

Derivative:

The derivative {eq}\dfrac{dy}{dx} {/eq} represents the rate of change in the value of y with respect to the rate of change in the value of x. The rate of change can be positive or negative.

Answer and Explanation:

The constant multiple rule of derivative represents the derivative of the function f(x) that is multiplied by a constant c.

{eq}\dfrac{d}{dx}[cf(x)] = c\dfrac{d}{dx}[f(x)] = cf'(x) {/eq}

The correct option is D.


Learn more about this topic:

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Derivatives: The Formal Definition

from Math 104: Calculus

Chapter 7 / Lesson 5
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