Final answer to the problem
$\frac{\left(2\cos\left(2x\right)+2\sin\left(2x\right)\right)\left(\sin\left(2x\right)+\cos\left(2x\right)\right)+\left(-\sin\left(2x\right)+\cos\left(2x\right)\right)\left(2\cos\left(2x\right)-2\sin\left(2x\right)\right)}{\left(\sin\left(2x\right)+\cos\left(2x\right)\right)^2}-3\sin\left(3x\right)$
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Step-by-step Solution
Learn how to solve sum rule of differentiation problems step by step online. Find the derivative d/dx((sin(2x)-cos(2x))/(sin(2x)+cos(2x))+cos(3x)) 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 cosine of a function is equal to minus the sine of the function times the derivative of the function, in other words, if f(x) = \cos(x), then f'(x) = -\sin(x)\cdot D_x(x). The derivative of the linear function times a constant, is equal to the constant. The derivative of the linear function is equal to 1.
Final answer to the problem
$\frac{\left(2\cos\left(2x\right)+2\sin\left(2x\right)\right)\left(\sin\left(2x\right)+\cos\left(2x\right)\right)+\left(-\sin\left(2x\right)+\cos\left(2x\right)\right)\left(2\cos\left(2x\right)-2\sin\left(2x\right)\right)}{\left(\sin\left(2x\right)+\cos\left(2x\right)\right)^2}-3\sin\left(3x\right)$
