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Find the derivative of $x^3+2x^2-63x$ 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 $x^3+2x^2-63x$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get
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$\lim_{h\to0}\left(\frac{\left(x+h\right)^3+2\left(x+h\right)^2-63\left(x+h\right)-\left(x^3+2x^2-63x\right)}{h}\right)$
Learn how to solve definition of derivative problems step by step online. Factor the expression x^3+2x^2-63x. Find the derivative of x^3+2x^2-63x 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+2x^2-63x. Substituting f(x+h) and f(x) on the limit, we get. Multiply the single term -63 by each term of the polynomial \left(x+h\right). Multiply the single term -1 by each term of the polynomial \left(x^3+2x^2-63x\right). Simplifying.