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Find the derivative of $30000x^3-11200x^2-11200x-11200$ 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 $30000x^3-11200x^2-11200x-11200$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get
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$\lim_{h\to0}\left(\frac{30000\left(x+h\right)^3-11200\left(x+h\right)^2-11200\left(x+h\right)-11200-\left(30000x^3-11200x^2-11200x-11200\right)}{h}\right)$
Learn how to solve definition of derivative problems step by step online. Find the derivative of 30000x^3-11200x^2-11200x+-11200 using the definition. Find the derivative of 30000x^3-11200x^2-11200x-11200 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 30000x^3-11200x^2-11200x-11200. Substituting f(x+h) and f(x) on the limit, we get. Multiply the single term -11200 by each term of the polynomial \left(x+h\right). Multiply the single term -1 by each term of the polynomial \left(30000x^3-11200x^2-11200x-11200\right). Add the values -11200 and 11200.