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Find the derivative of $\frac{x}{5}$ 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 $\frac{x}{5}$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get
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$\lim_{h\to0}\left(\frac{\frac{x+h}{5}-\frac{x}{5}}{h}\right)$
Learn how to solve definition of derivative problems step by step online. Find the derivative of (2x-9)/10+(2x-3)/(2x-1)=x/5 using the definition. Find the derivative of \frac{x}{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 \frac{x}{5}. Substituting f(x+h) and f(x) on the limit, we get. Combine \frac{x+h}{5}-\frac{x}{5} in a single fraction. Multiply -1 times 5. Multiplying the fraction by -5.