crealolobk

2021-12-10

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

levurdondishav4

Beginner2021-12-11Added 38 answers

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,

$\frac{df\left(x\right)}{dx}=\frac{d}{dx}\left(\frac{{x}^{2}}{3}\right)$

$\Rightarrow \frac{df}{dx}=\frac{2{x}^{1}}{3}$

$\Rightarrow \frac{df}{dx}=\frac{2x}{3}$

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$\frac{df}{dx}=\frac{2x}{3}$

The function:

Step 2:To determine

Derivative of the given function using power rule.

Step 3:Formula used

The power rule of derivative is given by:

Step 4:Solution

Consider the given function:

Differentiating with respect to x, we get,

Hence, the derivative of the given function is

Step 5:Conclusion

Hence, the derivative of the given function is