Question

question 1
let ( n ) be a nonzero real number. which of the following is equal to ( \frac{d}{dx}x^n )?
( \bigcirc (n - 1)x^n )
( \bigcirc nx^{n - 1} )
( \bigcirc (n - 1)x^{n - 1} )
( \bigcirc nx^n )

Explanation:

Step1: Recall the Power Rule of Differentiation

The power rule states that for a function \( y = x^n \) (where \( n \) is a real number), the derivative with respect to \( x \) is given by \( \frac{d}{dx}x^n = n x^{n - 1} \).

Step2: Apply the Power Rule to the Given Function

We are asked to find \( \frac{d}{dx}x^n \) where \( n \) is a non - zero real number. Using the power rule, we directly get \( \frac{d}{dx}x^n=nx^{n - 1} \).

Answer:

\( nx^{n - 1} \) (the option corresponding to \( nx^{n - 1} \))