"What is the derivative of x²?"

Question

"What is the derivative of x²?"

Asked on March 29, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

Accepted Answer · 2026-03-29T15:19:50.273Z

Step 1: Identify the function. The given function is $f(x) = x^2$. Step 2: Apply the power rule for differentiation. The power rule states that if $f(x) = x^n$, then its derivative $f'(x) = nx^{n-1}$. In this case, $n=2$. Step 3: Substitute $n=2$ into the power rule. $$ \frac{d}{dx}(x^2) = 2 \cdot x^{2-1} $$ Step 4: Simplify the expression. $$ 2 \cdot x^{2-1} = 2x^1 = 2x $$ The derivative of $x^2$ is: $$ \boxed{2x} $$

Accepted Answer · 2026-03-29T15:19:50.273Z

Step 1: Identify the function. The given function is $f(x) = x^2$. Step 2: Apply the power rule for differentiation. The power rule states that if $f(x) = x^n$, then its derivative $f'(x) = nx^{n-1}$. In this case, $n=2$. Step 3: Substitute $n=2$ into the power rule. $$ \frac{d}{dx}(x^2) = 2 \cdot x^{2-1} $$ Step 4: Simplify the expression. $$ 2 \cdot x^{2-1} = 2x^1 = 2x $$ The derivative of $x^2$ is: $$ \boxed{2x} $$