### Home > CALC > Chapter 9 > Lesson 9.3.1 > Problem9-82

9-82.

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

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

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

1. $\operatorname{tan} x$

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

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

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