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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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$\frac{d}{dx}\left(x\right)+\frac{d}{dx}\left(\sin\left(x\right)\right)+\frac{d}{dx}\left(\frac{\tan\left(x\right)}{x}\right)$

Learn how to solve problems step by step online. Find the derivative d/dx(x+sin(x)tan(x)/x) 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 the linear function is equal to 1. The derivative of the sine of a function is equal to the cosine of that function times the derivative of that function, in other words, if {f(x) = \sin(x)}, then {f'(x) = \cos(x)\cdot D_x(x)}. 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}}.

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