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Find the derivative of $dx^3+3x^2-2x-8$ 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 $dx^3+3x^2-2x-8$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get
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$\lim_{h\to0}\left(\frac{dx^3+3\left(x+h\right)^2-2\left(x+h\right)-8-\left(dx^3+3x^2-2x-8\right)}{h}\right)$
Learn how to solve definition of derivative problems step by step online. Find the derivative of dx^3+3x^2-2x+-8 using the definition. Find the derivative of dx^3+3x^2-2x-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 dx^3+3x^2-2x-8. Substituting f(x+h) and f(x) on the limit, we get. Multiply the single term -2 by each term of the polynomial \left(x+h\right). Multiply the single term -1 by each term of the polynomial \left(dx^3+3x^2-2x-8\right). Add the values -8 and 8.