### Home > CALC3RD > Chapter Ch9 > Lesson 9.3.1 > Problem9-82

9-82.

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

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

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

1. $\tan(x)$

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

1. $\sec^2(x)$

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