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Factor the sum of cubes: $a^3+b^3 = (a+b)(a^2-ab+b^2)$
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$derivdef\left(\frac{\left(x+3\right)\left(x^2-3x+9\right)}{x+3}\right)$
Learn how to solve definition of derivative problems step by step online. Find the derivative of (x^3+27)/(x+3) using the definition. Factor the sum of cubes: a^3+b^3 = (a+b)(a^2-ab+b^2). Simplify the fraction \frac{\left(x+3\right)\left(x^2-3x+9\right)}{x+3} by x+3. Find the derivative of x^2-3x+9 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 x^2-3x+9. Substituting f(x+h) and f(x) on the limit, we get. Expand \left(x+h\right)^2.