CPM Homework Help : CALC Problem 9-82

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

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

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

$\operatorname{tan} x$

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

$\operatorname{sec}^2(x)$

Hint:

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