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Let's solve the given problem step by step.

We are given:
\[
y = \frac{1}{3x^2}
\]
We need to find the derivative \(\frac{dy}{dx}\) at \(x = 1\).

### Step 1: Differentiate \( y = \frac{1}{3x^2} \)
We can rewrite \(y\) as:
\[
y = \frac{1}{3} x^{-2}
\]
Now, apply the power rule of differentiation. The power rule states that if \(y = x^n\), then \(\frac{dy}{dx} = n x^{n-1}\).

Using this rule:
\[
\frac{dy}{dx} = \frac{1}{3} \cdot (-2) x^{-3} = -\frac{2}{3x^3}
\]

### Step 2: Evaluate at \(x = 1\)
Now, substitute \(x = 1\) into the derivative expression:
\[
\frac{dy}{dx} \bigg|_{x=1} = -\frac{2}{3(1)^3}

Find the derivative of the function y = 1/(3x^2) using the power rule of differentiation and evaluate dy/dx at x = 1. Suitable for high school students in Grades 10-12.

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