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 $f'(x) =2x$.