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Simplify the derivative by applying the properties of logarithms
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$\frac{d}{dx}\left(\ln\left(\left(x^2+1\right)^2\right)^2\right)$
Learn how to solve problems step by step online. Find the derivative using logarithmic differentiation method d/dx(ln(1/((x^2+1)^2))^2). Simplify the derivative by applying the properties of logarithms. Using the power rule of logarithms: \log_a(x^n)=n\cdot\log_a(x). The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function.