Mathematics

The key is to apply the product rule twice, treating $x^2$ and $\arctan x$ as separate pieces that both change. On the first derivative, you'll get a sum of two terms; on the second derivative, you'll need to differentiate each of those terms again using the product rule. Watch for the derivative of $\arctan x$, which is $\frac{1}{1+x^2}$, and look for opportunities to combine fractions with a common denominator at the end.

The key is to apply the product rule twice, treating $x^2$ and $\arctan x$ as separate pieces that both change. On the first derivative, you'll get a sum of two terms; on the second derivative, you'll need to differentiate each of those terms again using the product rule. Watch for the derivative of $\arctan x$, which is $\frac{1}{1+x^2}$, and look for opportunities to combine fractions with a common denominator at the end.