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Calculate the square root of $45$
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$derivdef\left(\log_{5}\left(3\sqrt{5}\right)\right)$
Learn how to solve definition of derivative problems step by step online. Find the derivative of log5(45^0.5) using the definition. Calculate the square root of 45. Find the derivative of \log_{5}\left(3\sqrt{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_{5}\left(3\sqrt{5}\right). Substituting f(x+h) and f(x) on the limit, we get. Cancel like terms \log_{5}\left(3\sqrt{5}\right) and -\log_{5}\left(3\sqrt{5}\right). Zero divided by anything is equal to zero.