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Simplify the derivative by applying the properties of logarithms
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$\frac{d}{dx}\left(\left(5x^{2}\right)^3\ln\left(x^2+1\right)\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative using logarithmic differentiation method (5x^(3-1))^3ln(x^2+1). Simplify the derivative by applying the properties of logarithms. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=. 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.