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The product of two binomials of the form $(x+a)(x+b)$ is equal to the product of the first terms of the binomials, plus the algebraic sum of the second terms by the common term of the binomials, plus the product of the second terms of the binomials. In other words: $(x+a)(x+b)=x^2+(a+b)x+ab$
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$derivdef\left(a^2+\left(15-7\right)a+15\cdot -7\right)$
Learn how to solve definition of derivative problems step by step online. Find the derivative of (a+15)(a-7) using the definition. The product of two binomials of the form (x+a)(x+b) is equal to the product of the first terms of the binomials, plus the algebraic sum of the second terms by the common term of the binomials, plus the product of the second terms of the binomials. In other words: (x+a)(x+b)=x^2+(a+b)x+ab. Subtract the values 15 and -7. Multiply 15 times -7. Find the derivative of a^2+8a-105 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 a^2+8a-105. Substituting f(x+h) and f(x) on the limit, we get.