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Find the derivative of $4mn+n^2+4m^2$ 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 $4mn+n^2+4m^2$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get
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$\lim_{h\to0}\left(\frac{4m\left(n+h\right)+\left(n+h\right)^2+4m^2-\left(4mn+n^2+4m^2\right)}{h}\right)$
Learn how to solve definition of derivative problems step by step online. Factor the expression 4mn+n^24m^2. Find the derivative of 4mn+n^2+4m^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 4mn+n^2+4m^2. Substituting f(x+h) and f(x) on the limit, we get. Expand \left(n+h\right)^2. Multiply the single term -1 by each term of the polynomial \left(4mn+n^2+4m^2\right). Simplifying.