Question

Find the derivative of $x^2$ using first principle.

• A. $2x^2$
• B. $\frac{x}{2}$
• C. $2x$
• D. $\frac{x^2}{2}$

Answer 1

The correct option is C $2x$

${lim}_{h\to 0}\frac{\left(\right(x+h{)}^2-x^2)}{h}$ $={lim}_{h\to 0}\frac{\left(\right(x+h-x\left)\right(x+h+x\left)\right)}{h}$ $={lim}_{h\to 0}(2x+h)=2x+0=2x$