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