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The derivative of a sum of two or more functions is the sum of the derivatives of each function
Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$, where $f=\arctan\left(x\right)$ and $g=\ln\left(1+x^2\right)$
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$\frac{d}{dx}\left(\frac{\sin\left(x\right)}{1+\cos\left(x\right)}\right)+\frac{d}{dx}\left(\arctan\left(x\right)\ln\left(1+x^2\right)\right)$
Learn how to solve sum rule of differentiation problems step by step online. Find the derivative d/dx((sin(x)/(1+cos(x))+arctan(x)ln(1+x^2)) using the sum rule. The derivative of a sum of two or more functions is the sum of the derivatives of each function. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=\arctan\left(x\right) and g=\ln\left(1+x^2\right). The derivative of the natural logarithm of a function is equal to the derivative of the function divided by that function. If f(x)=ln\:a (where a is a function of x), then \displaystyle f'(x)=\frac{a'}{a}. 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}}.