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