Final Answer
$1$
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Step-by-step Solution
Problem to solve:
$derivdef\left(x\right)$
1
Find the derivative of $x$ using the definition. 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 $x$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get
$\lim_{h\to0}\left(\frac{h}{h}\right)$
2
Simplify the fraction $\frac{h}{h}$ by $h$
$\lim_{h\to0}\left(1\right)$
3
The limit of a constant is just the constant
$1$
Final Answer
$1$