Use formulas (1) and (2) and the power rule to find the derivatives of f(x)=x23

Step 1:Given
The function:
${\displaystyle f\left(x\right)=\frac{x^2}{3}}$
Step 2:To determine
Derivative of the given function using power rule.
Step 3:Formula used
The power rule of derivative is given by:
${\displaystyle \frac{d}{dx}\left(x^n\right)=n{x}^{n-1}}$
Step 4:Solution
Consider the given function:
${\displaystyle f\left(x\right)=\frac{x^2}{3}}$
Differentiating with respect to x, we get,
${\displaystyle \frac{df\left(x\right)}{dx}=\frac{d}{dx}\left(\frac{x^2}{3}\right)}$
${\displaystyle \Rightarrow \frac{df}{dx}=\frac{2x^1}{3}}$
${\displaystyle \Rightarrow \frac{df}{dx}=\frac{2x}{3}}$
Hence, the derivative of the given function is ${\displaystyle \frac{df}{dx}=\frac{2x}{3}}$
Step 5:Conclusion
Hence, the derivative of the given function is ${\displaystyle \frac{df}{dx}=\frac{2x}{3}}$