Question

Find the derivatives of$f\left(x\right)=x^2.$

Short answer

The derivative of$f\left(x\right)=x^2$is$2x.$

Step-by-step solution

Given Information    

The given expression is $f\left(x\right)=x^2.$

Simplification 

$$\begin{gathered} f\text{'}\left(x\right)=\underset{h\to 0}{\lim }\frac{f(x+h)-f\left(x\right)}{h} \\ =\underset{h\to 0}{\lim }\frac{{(x+h)}^2-x^2}{h} \\ =\underset{h\to 0}{\lim }\frac{x^2+2hx+h^2-x^2}{h} \\ =\underset{h\to 0}{\lim }\frac{(2x+h)h}{h} \\ =2x \\ Therefore,thederivateoff\left(x\right)=x^{2}is2x. \end{gathered}$$