crealolobk

2021-12-10

Use formulas (1) and (2) and the power rule to find the derivatives of $f\left(x\right)=\frac{{x}^{2}}{3}$

### Answer & Explanation

levurdondishav4

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

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