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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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$\frac{d}{dx}\left(\cot\left(3x\right)\right)+\frac{d}{dx}\left(x\sin\left(x^3+5\right)\right)$
Learn how to solve differential calculus problems step by step online. Find the derivative d/dx(cot(3x)+xsin(x^3+5)) 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=x and g=\sin\left(x^3+5\right). 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)}.