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The difference of the squares of two terms, divided by the sum of the same terms, is equal to the difference of the terms. In other words: $\displaystyle\frac{a^2-b^2}{a+b}=a-b$.
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$derivdef\left(t-8\right)$
Learn how to solve definition of derivative problems step by step online. Find the derivative of (t^2-64)/(t+8) using the definition. The difference of the squares of two terms, divided by the sum of the same terms, is equal to the difference of the terms. In other words: \displaystyle\frac{a^2-b^2}{a+b}=a-b.. Find the derivative of t-8 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 t-8. Substituting f(x+h) and f(x) on the limit, we get. Multiply the single term -1 by each term of the polynomial \left(t-8\right). Add the values -8 and 8.