Question

Find the derivative \( f'(x) \) where \( f(x)=x^2 \).

Answer 1

In this problem, we need to find the derivative of the given function. The given function is:

\( f(x)=x^2 \)

According to the power rule of derivatives:

\( \frac{d}{dx}(x^n)=nx^{n-1} \)

Substituting \( n=2 \) in the above formula, we get:

\( \frac{d}{dx}(x^2)=2x^{2-1} \)

\( \implies \frac{d}{dx}(x^2)=2x^{1} \)

\( \implies \frac{d}{dx}(x^2)=2x \)

\( \implies \boxed{f'(x)=2x } \)

The derivative of the given function is \( f'(x) =2x \).