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Divide $1$ by $5$
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$derivdef\left(\log_{25}\left(\frac{1}{5}\right)\right)$
Learn how to solve definition of derivative problems step by step online. Find the derivative of log25((1/5)) using the definition. Divide 1 by 5. Find the derivative of \log_{25}\left(\frac{1}{5}\right) 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 \log_{25}\left(\frac{1}{5}\right). Substituting f(x+h) and f(x) on the limit, we get. Cancel like terms \log_{25}\left(\frac{1}{5}\right) and -\log_{25}\left(\frac{1}{5}\right). Zero divided by anything is equal to zero.