Find the derivative $\frac{d}{dx}\left(\frac{1}{x+1}+x^{-1}+\ln\left(x+1\right)-x^{-2}\right)$ using the sum rule

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$\frac{d}{dx}\left(\frac{1}{x+1}\right)+\frac{d}{dx}\left(x^{-1}\right)+\frac{d}{dx}\left(\ln\left(x+1\right)\right)+\frac{d}{dx}\left(-x^{-2}\right)$

Learn how to solve sum rule of differentiation problems step by step online. Find the derivative d/dx(1/(x+1)+x^(-1)ln(x+1)-x^(-2)) using the sum rule. 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}. The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If f(x)=ln\:a (where a is a function of x), then \displaystyle f'(x)=\frac{a'}{a}.