Match the rule with the title. \frac{\mathrm{d} }{\mathrm{d} x} \left [x^n\right ]= nx^{n - 1} A....


Match the rule with the title.

{eq}\frac{\mathrm{d} }{\mathrm{d} x} \left [x^n\right ]= nx^{n - 1} {/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

Rules of Derivative:

To evaluate the rate of change of any function i.e. the derivative of a function, we have many rules that make our work easier. These rules are derived from the limit definition of derivative which states that the derivative of function {eq}f(x) {/eq} is equal to

{eq}f'(x)=\lim_{h \rightarrow} \dfrac{f(x+h)-f(x)}{h} {/eq}

Answer and Explanation:

The given rule {eq}\frac{\mathrm{d} }{\mathrm{d} x} \left [x^n\right ]= nx^{n - 1} {/eq} is a power rule of derivative.

Power rule of derivative states that whenever we have any function in the form of {eq}x^n {/eq} where n is any real number, the derivative of the function is calculated by using the formula {eq}\dfrac{\mathrm{d} }{\mathrm{d} x} \left [x^n\right ]= nx^{n - 1} {/eq}

So, the correct answer is {eq}\color{blue}{C.} {/eq}

Learn more about this topic:

Power Rule for Derivatives: Examples & Explanation

from High School Precalculus: Help and Review

Chapter 19 / Lesson 18

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