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** Step-by-step Solution **

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

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

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

Learn how to solve definition of derivative problems step by step online. Factor the expression 2x^2+ax. Find the derivative of 2x^2+ax 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^2+ax. Substituting f(x+h) and f(x) on the limit, we get. Multiply the single term x by each term of the polynomial \left(a+h\right). Multiply the single term -1 by each term of the polynomial \left(2x^2+ax\right). Simplifying.

** Final Answer

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