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Find the derivative of $\frac{x+1}{2}$ 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 $\frac{x+1}{2}$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get
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$\lim_{h\to0}\left(\frac{\frac{x+h+1}{2}-\frac{x+1}{2}}{h}\right)$
Learn how to solve problems step by step online. Find the derivative of (x+1)/2 using the definition. Find the derivative of \frac{x+1}{2} 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{x+1}{2}. Substituting f(x+h) and f(x) on the limit, we get. Combine \frac{x+h+1}{2}-\frac{x+1}{2} in a single fraction. Multiply -1 times 2. Multiplying the fraction by -2.