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Find the derivative of $\frac{x}{4}$ 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 $\frac{x}{4}$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get
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$\lim_{h\to0}\left(\frac{\frac{x+h}{4}-\frac{x}{4}}{h}\right)$
Learn how to solve definition of derivative problems step by step online. Find the derivative of x/4 using the definition. Find the derivative of \frac{x}{4} 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}{4}. Substituting f(x+h) and f(x) on the limit, we get. Combine \frac{x+h}{4}-\frac{x}{4} in a single fraction. Multiply -1 times 4. Multiplying the fraction by -4.