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The derivative of a sum of two or more functions is the sum of the derivatives of each function
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$\frac{d}{dx}\left(\frac{1}{x}\right)+\frac{d}{dx}\left(\frac{1}{4}\right)+\frac{d}{dx}\left(\frac{-11}{14x}\right)$
Learn how to solve problems step by step online. Find the derivative of 3/(4x)-5/14-8/(7x)=1/x+1/4-11/(14x). 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 (\frac{1}{4}) 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}}. 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}}.