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Find the derivative of $x^3-4x^2-31x-70$ 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 $x^3-4x^2-31x-70$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get
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$\lim_{h\to0}\left(\frac{\left(x+h\right)^3-4\left(x+h\right)^2-31\left(x+h\right)-70-\left(x^3-4x^2-31x-70\right)}{h}\right)$
Learn how to solve problems step by step online. Find the derivative of x^3-4x^2-31x+-70 using the definition. Find the derivative of x^3-4x^2-31x-70 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^3-4x^2-31x-70. Substituting f(x+h) and f(x) on the limit, we get. Multiply the single term -31 by each term of the polynomial \left(x+h\right). Multiply the single term -1 by each term of the polynomial \left(x^3-4x^2-31x-70\right). Add the values -70 and 70.