Implicit differentiation and inverse trigonometric functions practice question 12

$g$ is a product, and one factor is $1 + x^{2}$. Which rule applies, and what sits in the denominator of the derivative of $\arctan x$?

Product rule, and $\dfrac{d}{dx}\arctan x = \dfrac{1}{1 + x^{2}}$. Notice how the second term simplifies.

$\arctan 1 = \pi/4$.