Find the derivative $\frac{d}{dx}\left(\frac{5}{\sqrt[3]{x^4}}+\frac{-6}{x}+\frac{3}{8\sqrt{x}}-5\right)$ using the sum rule

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$\frac{d}{dx}\left(\frac{5}{\sqrt[3]{x^{4}}}+\frac{-6}{x}+\frac{3}{8\sqrt{x}}-5\right)$

Learn how to solve problems step by step online. Find the derivative d/dx(5/(x^4^1/3)+-6/x3/(8x^1/2)+-5) using the sum rule. Simplify the derivative by applying the properties of logarithms. The derivative of a sum of two or more functions is the sum of the derivatives of each function. The derivative of the constant function (-5) is equal to zero. 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}}.