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Find the derivative of $-4x^2+8x-5$ 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 $-4x^2+8x-5$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get
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$\lim_{h\to0}\left(\frac{-4\left(x+h\right)^2+8\left(x+h\right)-5-\left(-4x^2+8x-5\right)}{h}\right)$
Learn how to solve problems step by step online. Find the derivative of f=-4x^2+8x+-5 using the definition. Find the derivative of -4x^2+8x-5 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 -4x^2+8x-5. Substituting f(x+h) and f(x) on the limit, we get. Multiply the single term 8 by each term of the polynomial \left(x+h\right). Multiply the single term -1 by each term of the polynomial \left(-4x^2+8x-5\right). Add the values -5 and 5.