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