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A binomial squared (difference) is equal to the square of the first term, minus the double product of the first by the second, plus the square of the second term. In other words: $(a-b)^2=a^2-2ab+b^2$
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$derivdef\left(2x-3\left(x^2-6x+9\right)\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of 2x-3(x-3)^2 using the definition. A binomial squared (difference) is equal to the square of the first term, minus the double product of the first by the second, plus the square of the second term. In other words: (a-b)^2=a^2-2ab+b^2. Multiply the single term -3 by each term of the polynomial \left(x^2-6x+9\right). Combining like terms 2x and 18x. Find the derivative of 20x-3x^2-27 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 20x-3x^2-27. Substituting f(x+h) and f(x) on the limit, we get.