Final Answer
Step-by-step Solution
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Using the power rule of logarithms: $\log_a(x^n)=n\cdot\log_a(x)$
Learn how to solve logarithmic differentiation problems step by step online.
$\frac{d}{dx}\left(\frac{2\ln\left(x\right)}{x^2}\right)$
Learn how to solve logarithmic differentiation problems step by step online. Find the derivative using logarithmic differentiation method d/dx(ln(x^2)/(x^2)). Using the power rule of logarithms: \log_a(x^n)=n\cdot\log_a(x). Apply the quotient rule for differentiation, which states that if f(x) and g(x) are functions and h(x) is the function defined by {\displaystyle h(x) = \frac{f(x)}{g(x)}}, where {g(x) \neq 0}, then {\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}. Simplify \left(x^2\right)^2 using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 2 and n equals 2. The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function.