Question

Fill in the blank:

$\frac{d}{dx}\left(x^k\right)=---$ ($k$ is a constant)

Short answer

$\frac{d}{dx}\left(x^k\right)=k{x}^{k-1}$

Step-by-step solution

Given Information

The given expression is$\frac{d}{dx}\left(x^k\right)$

Simplification

Power Rule states that $\frac{d}{dx}\left(x^n\right)=n{x}^{n-1}$, where $n$is real number,

$\frac{d}{dx}\left(x^k\right)$, $k$is a constant (real)

Hence, power rule also applies here.

$\frac{d}{dx}\left(x^k\right)=k{x}^{k-1}$