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Find the derivative of $3m^2-6mn+4m-8n$ 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 $3m^2-6mn+4m-8n$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get
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$\lim_{h\to0}\left(\frac{3m^2-6m\left(n+h\right)+4m-8\left(n+h\right)-\left(3m^2-6mn+4m-8n\right)}{h}\right)$
Learn how to solve definition of derivative problems step by step online. Find the derivative of 3m^2-6mn4m-8n using the definition. Find the derivative of 3m^2-6mn+4m-8n 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 3m^2-6mn+4m-8n. Substituting f(x+h) and f(x) on the limit, we get. Multiply the single term -8 by each term of the polynomial \left(n+h\right). Multiply the single term -1 by each term of the polynomial \left(3m^2-6mn+4m-8n\right). Simplifying.