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Find the derivative of $\log_{2}\left(\frac{93}{10}\right)$ 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 $\log_{2}\left(\frac{93}{10}\right)$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get
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$\lim_{h\to0}\left(\frac{\log_{2}\left(\frac{93}{10}\right)-\log_{2}\left(\frac{93}{10}\right)}{h}\right)$
Learn how to solve definition of derivative problems step by step online. Find the derivative of log2(x)-log2(10)=log2(9.3) using the definition. Find the derivative of \log_{2}\left(\frac{93}{10}\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_{2}\left(\frac{93}{10}\right). Substituting f(x+h) and f(x) on the limit, we get. Cancel like terms \log_{2}\left(\frac{93}{10}\right) and -\log_{2}\left(\frac{93}{10}\right). Zero divided by anything is equal to zero. The limit of a constant is just the constant.