Determine the derivative of 𝑦𝑥=𝑥2 at the point xQuestion 8Answera.2𝑥b.𝑥2c.2d.2𝑥2

Step 1: Break Down the Problem

We need to determine the derivative of the function $y = x^2$ at a specific point on the x-axis.

Step 2: Relevant Concepts

The derivative of a function $f(x)$ is given by the formula: $f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}$ For the function $y = x^2$, we will differentiate using the power rule: $\frac{d}{dx}(x^n) = n \cdot x^{n-1}$

Step 3: Analysis and Detail

1. Differentiate $y = x^2$:
   • Using the power rule: $\frac{dy}{dx} = 2 \cdot x^{2-1} = 2x$

Step 4: Verify and Summarize

The derivative $\frac{dy}{dx}$ when evaluated at any point $x$ is $2x$.

Final Answer

The derivative of $y = x^2$ is $2x$.

Thus, the answer is (a) $2x$.