Question

If f(x)=x², what is the derivative of f(x) at x=??

• A. 24
• B. 12
• C. 0
• D. 4

Answer 1

Answer: (D)

4

Answer 2

To find the derivative of $f(x) = x^2$ at $x=2$, we follow these steps:

1. Find the general derivative of the function $f(x)$: The given function is $f(x) = x^2$. We use the power rule of differentiation, which states that if $f(x) = x^n$, then its derivative $f'(x) = nx^{n-1}$. For $f(x) = x^2$, here $n=2$. So, the derivative $f'(x) = 2 \cdot x^{2-1} = 2x^1 = 2x$.

2. Evaluate the derivative at the specified point $x=2$: Now, substitute $x=2$ into the derivative function $f'(x) = 2x$. $f'(2) = 2 \times 2 = 4$.

Thus, the derivative of $f(x) = x^2$ at $x=2$ is 4.