CPM Homework Help : APCALC Problem 9-82

$\lim \limits _ { h \rightarrow 0 } \frac { \operatorname { tan } ^ { - 1 } ( x + h ) - \operatorname { tan } ^ { - 1 } ( x ) } { h }$ is equivalent to:

$\frac { 1 } { 1 + x ^ { 2 } }$

$\frac { 1 } { x \sqrt { x ^ { 2 } - 1 } }$

$\tan(x)$

$\frac { 1 } { x \sqrt { 1 - x ^ { 2 } } }$

$\sec^2(x)$

Hint:

This is the definition of derivative for $\tan^{–1}(x)$ .