Final answer to the problem
$\frac{\cos\left(5x\right)}{1+x^2}-5\arctan\left(x\right)\sin\left(5x\right)$
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Step-by-step Solution
Learn how to solve product rule of differentiation problems step by step online. Find the derivative of arctan(x)cos(5x). Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=\arctan\left(x\right) and g=\cos\left(5x\right). 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
$\frac{\cos\left(5x\right)}{1+x^2}-5\arctan\left(x\right)\sin\left(5x\right)$
