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Find the derivative of $27+27x+9x^2+x^3$ 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 $27+27x+9x^2+x^3$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get
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$\lim_{h\to0}\left(\frac{27+27\left(x+h\right)+9\left(x+h\right)^2+\left(x+h\right)^3-\left(27+27x+9x^2+x^3\right)}{h}\right)$
Learn how to solve problems step by step online. Find the derivative of 27+27x9x^2x^3 using the definition. Find the derivative of 27+27x+9x^2+x^3 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 27+27x+9x^2+x^3. Substituting f(x+h) and f(x) on the limit, we get. Multiply the single term 27 by each term of the polynomial \left(x+h\right). Multiply the single term -1 by each term of the polynomial \left(27+27x+9x^2+x^3\right). Add the values 27 and -27.