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Simplify the derivative by applying the properties of logarithms
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$\frac{d}{dx}\left(\frac{1}{2}x^2\ln\left(x^2+1\right)^{10}\ln\left(x\right)\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative using logarithmic differentiation method ln(x^1/2)ln(e^x^2)ln(x^2+1)^10. Simplify the derivative by applying the properties of logarithms. The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g'. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}.