Solved example of definition of derivative
Apply the definition of the derivative: $\displaystyle f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}$. The function $f(x)$ is the function we want to differentiate, which is $x^2$. Substituting $f(x+h)$ and $f(x)$ on the limit
Expand $\left(x+h\right)^2$
Factoring by $h$
Simplify the fraction $\frac{h\left(h+2x\right)}{h}$ by $h$
Evaluate the limit by replacing all occurrences of $h$ by $0$
Access detailed step by step solutions to thousands of problems, growing every day!