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The derivative of a sum of two or more functions is the sum of the derivatives of each function
Learn how to solve integrals of rational functions problems step by step online.
$\frac{d}{dx}\left(\frac{\left(x+4\right)^2}{x^2+4x}\right)+\frac{d}{dx}\left(\frac{\left(x-4\right)^2}{x^2-4x}\right)$
Learn how to solve integrals of rational functions problems step by step online. Find the derivative using the quotient rule ((x+4)^2)/(x^2+4x)+((x-4)^2)/(x^2-4x). The derivative of a sum of two or more functions is the sum of the derivatives of each function. 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}}. 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}}. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}.