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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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$derivdef\left(x^2-4x+4+4\left(y+1\right)\right)$
Learn how to solve problems step by step online. Find the derivative of (x-2)^2+4(y+1) 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 4 by each term of the polynomial \left(y+1\right). Add the values 4 and 4. Find the derivative of x^2-4x+8+4y 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^2-4x+8+4y. Substituting f(x+h) and f(x) on the limit, we get.