Let's differentiate the first term, $g(x) = x \arctan (5x)$.
Using the product rule, $(uv)' = u'v + uv'$, where $u = x$ and $v = \arctan (5x)$.
Then $u' = \frac{d}{dx}(x) = 1$.
For $v' = \frac{d}{dx}(\arctan (5x))$, we use the chain rule. The derivative of
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