Find the derivative of $f(x)=x^2$.

Step 1: Recall the Power Rule

To find the derivative of $f(x) = x^2$, we can use the power rule for differentiation. The power rule states that the derivative of $x$ raised to the power of $n$ is $n$ times $x$ raised to the power of $n-1$. In our case, $n=2$.

Step 2: Apply the Power Rule

Now, we apply the power rule by substituting $n=2$ into the formula. This means we bring the exponent $2$ down as a coefficient and subtract $1$ from the exponent.

Step 3: Simplify the expression

Finally, we simplify the expression. $2-1$ equals $1$, so $x^{2-1}$ becomes $x^1$, which is simply $x$. Therefore, the derivative of $x^2$ is $2x$.

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