|
Derivative of $$$x^{n}$$$ with respect to $$$x$$$
Related calculators: Logarithmic Differentiation Calculator, Implicit Differentiation Calculator with Steps
Your Input
Find $$$\frac{d}{dx} \left(x^{n}\right)$$$.
Solution
Apply the power rule $$$\frac{d}{dx} \left(x^{m}\right) = m x^{m - 1}$$$ with $$$m = n$$$:
$${\color{red}\left(\frac{d}{dx} \left(x^{n}\right)\right)} = {\color{red}\left(n x^{n - 1}\right)}$$Simplify:
$$n x^{n - 1} = \frac{n x^{n}}{x}$$Thus, $$$\frac{d}{dx} \left(x^{n}\right) = \frac{n x^{n}}{x}$$$.
Answer
$$$\frac{d}{dx} \left(x^{n}\right) = \frac{n x^{n}}{x}$$$A