"Use formulas (1) and (2) and the power..." was answered by our community

crealolobk

Answered question

2021-12-10

Use formulas (1) and (2) and the power rule to find the derivatives of

f (x) = \frac{x^{2}}{3}

levurdondishav4

Beginner2021-12-11Added 38 answers

Step 1:Given
The function:

f (x) = \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}{d x} (x^{n}) = n x^{n - 1}

Step 4:Solution
Consider the given function:

f (x) = \frac{x^{2}}{3}

Differentiating with respect to x, we get,

\frac{d f (x)}{d x} = \frac{d}{d x} (\frac{x^{2}}{3})

\Rightarrow \frac{d f}{d x} = \frac{2 x^{1}}{3}

\Rightarrow \frac{d f}{d x} = \frac{2 x}{3}

Hence, the derivative of the given function is

\frac{d f}{d x} = \frac{2 x}{3}

Step 5:Conclusion
Hence, the derivative of the given function is

\frac{d f}{d x} = \frac{2 x}{3}

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