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Find the derivative of $x^2$ 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 $x^2$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get

Learn how to solve definition of derivative problems step by step online.

$\lim_{h\to0}\left(\frac{\left(x+h\right)^2-x^2}{h}\right)$

Learn how to solve definition of derivative problems step by step online. Find the derivative of x^2 using the definition. Find the derivative of x^2 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^2. Substituting f(x+h) and f(x) on the limit, we get. Expand \left(x+h\right)^2. Cancel like terms x^2 and -x^2. Factor the polynomial 2xh+h^2 by it's greatest common factor (GCF): h.

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