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Take $\frac{-\frac{1}{3}}{2}$ out of the fraction
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$\frac{d}{dx}\left(-\frac{1}{6}x^2-\frac{1}{2}\ln\left(1+x^2\right)\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative of (-1/3x^2)/2-1/2ln(1+x^2). Take \frac{-\frac{1}{3}}{2} out of the fraction. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}.