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Simplify the derivative by applying the properties of logarithms
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$\frac{d}{dx}\left(\frac{-2y}{x+1}=\left(x+1\right)^3\right)$
Learn how to solve classify algebraic expressions problems step by step online. Find the implicit derivative d/dx(-2/(x+1)y=(x+1)^3). Simplify the derivative by applying the properties of logarithms. Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. Apply the quotient rule for differentiation, which states that if f(x) and g(x) are functions and h(x) is the function defined by {\displaystyle h(x) = \frac{f(x)}{g(x)}}, where {g(x) \neq 0}, then {\displaystyle h'(x) = \frac{f'(x) \cdot g(x) - g'(x) \cdot f(x)}{g(x)^2}}.