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Using the power rule of logarithms: $\log_a(x^n)=n\cdot\log_a(x)$
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$derivdef\left(2\ln\left(x\right)\right)$
Learn how to solve problems step by step online. Find the derivative of ln(x^2) using the definition. Using the power rule of logarithms: \log_a(x^n)=n\cdot\log_a(x). Find the derivative of 2\ln\left(x\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 2\ln\left(x\right). Substituting f(x+h) and f(x) on the limit, we get. Factor the polynomial 2\ln\left(x+h\right)-2\ln\left(x\right) by it's greatest common factor (GCF): 2. The limit of the product of a function and a constant is equal to the limit of the function, times the constant: \displaystyle \lim_{t\to 0}{\left(at\right)}=a\cdot\lim_{t\to 0}{\left(t\right)}.