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Factor the difference of cubes: $a^3-b^3 = (a-b)(a^2+ab+b^2)$
Learn how to solve definition of derivative problems step by step online.
$derivdef\left(\frac{\left(x-1\right)\left(x^2+x+1\right)}{x-1}\right)$
Learn how to solve definition of derivative problems step by step online. Find the derivative of (x^3-1)/(x-1) using the definition. Factor the difference of cubes: a^3-b^3 = (a-b)(a^2+ab+b^2). Simplify the fraction \frac{\left(x-1\right)\left(x^2+x+1\right)}{x-1} by x-1. Find the derivative of x^2+x+1 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+x+1. Substituting f(x+h) and f(x) on the limit, we get. Expand \left(x+h\right)^2.