Final answer to the problem
Step-by-step Solution
Specify the solving method
Find the derivative of $2x$ 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 $2x$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get
Learn how to solve definition of derivative problems step by step online.
$\lim_{h\to0}\left(\frac{2\left(x+h\right)-2x}{h}\right)$
Learn how to solve definition of derivative problems step by step online. Find the derivative of (x+1)/x=2x using the definition. Find the derivative of 2x 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 2x. Substituting f(x+h) and f(x) on the limit, we get. Multiply the single term 2 by each term of the polynomial \left(x+h\right). Simplifying. Simplify the fraction \frac{2h}{h} by h.