Find the derivative $\frac{d}{dx}\left(8\sqrt{x}+\frac{7}{x^5}\right)$ using the sum rule

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$\frac{d}{dx}\left(8\sqrt{x}\right)+\frac{d}{dx}\left(\frac{7}{x^5}\right)$

Learn how to solve sum rule of differentiation problems step by step online. Find the derivative (d/dx)(8x^1/2+7/(x^5)) 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 (8) 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}. 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}}.