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

Question

Determine the derivative of 𝑦𝑥=𝑥² at the point x

Question 8

Answer
a. 2𝑥
b. 𝑥²
c. 2
d. 2𝑥²

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Solution

Step 1: Break Down the Problem

We need to determine the derivative of the function y=x2 y = x^2 at a specific point on the x-axis.

Step 2: Relevant Concepts

The derivative of a function f(x) f(x) is given by the formula: f(x)=limh0f(x+h)f(x)h f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h} For the function y=x2 y = x^2 , we will differentiate using the power rule: ddx(xn)=nxn1 \frac{d}{dx}(x^n) = n \cdot x^{n-1}

Step 3: Analysis and Detail

  1. Differentiate y=x2 y = x^2 :
    • Using the power rule: dydx=2x21=2x \frac{dy}{dx} = 2 \cdot x^{2-1} = 2x

Step 4: Verify and Summarize

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

Final Answer

The derivative of y=x2 y = x^2 is 2x 2x .

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

This problem has been solved

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