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Find the derivative of $100k^3+40k^2+4k$ 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 $100k^3+40k^2+4k$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get
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$\lim_{h\to0}\left(\frac{100\left(k+h\right)^3+40\left(k+h\right)^2+4\left(k+h\right)-\left(100k^3+40k^2+4k\right)}{h}\right)$
Learn how to solve definition of derivative problems step by step online. Find the derivative of 100k^3+40k^24k using the definition. Find the derivative of 100k^3+40k^2+4k 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 100k^3+40k^2+4k. Substituting f(x+h) and f(x) on the limit, we get. Multiply the single term 4 by each term of the polynomial \left(k+h\right). Multiply the single term -1 by each term of the polynomial \left(100k^3+40k^2+4k\right). Simplifying.