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Factor the sum or difference of cubes using the formula: $a^3\pm b^3 = (a\pm b)(a^2\mp ab+b^2)$
Learn how to solve definition of derivative problems step by step online.
$derivdef\left(\frac{\left(2a-1\right)\left(4a^{2}+2a+1\right)}{2a-1}\right)$
Learn how to solve definition of derivative problems step by step online. Find the derivative of (8a^3-1)/(2a-1) using the definition. Factor the sum or difference of cubes using the formula: a^3\pm b^3 = (a\pm b)(a^2\mp ab+b^2). Simplify the fraction \frac{\left(2a-1\right)\left(4a^{2}+2a+1\right)}{2a-1} by 2a-1. Find the derivative of 4a^{2}+2a+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 4a^{2}+2a+1. Substituting f(x+h) and f(x) on the limit, we get. Multiply the single term 2 by each term of the polynomial \left(a+h\right).