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Find the derivative of $a^3+b^3$ 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 $a^3+b^3$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get
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$\lim_{h\to0}\left(\frac{a^3+\left(b+h\right)^3-\left(a^3+b^3\right)}{h}\right)$
Learn how to solve definition of derivative problems step by step online. Find the derivative of a^3+b^3 using the definition. Find the derivative of a^3+b^3 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^3+b^3. Substituting f(x+h) and f(x) on the limit, we get. Multiply the single term -1 by each term of the polynomial \left(a^3+b^3\right). Simplifying. Factor the sum or difference of cubes using the formula: a^3\pm b^3 = (a\pm b)(a^2\mp ab+b^2).