$\text { Find the derivative of the function } f ( x ) = \operatorname { arcsec } ( 9 x ) \text {. }$
A)$-\frac { 1 } { | 9 x | \sqrt { 81 x ^ { 2 } - 1 } }$
B)$ \frac { 1 } { | x | \sqrt { 81 x ^ { 2 } - 1 } }$
C)$\frac { 1 } { | 9 x | \sqrt { 81 x ^ { 2 } - 1 } }$
D)$\frac { 1 } { \sqrt { 81 x ^ { 2 } + 1 } }$
E)$- \frac { 1 } { | x | \sqrt { 81 x ^ { 2 } - 1 } }$

Question

Quizplus · Accepted Answer

We use the formula $\frac{d}{dx}	ext{arcsec}(u)=\frac{1}{|u|\sqrt{u^2-1}}\cdot \frac{du}{dx}$, where $u=9x$. Therefore, $\frac{du}{dx}=9$, so $$\frac{d}{dx}	ext{arcsec}(9x)=\frac{1}{|9x|\sqrt{(9x)^2-1}}\cdot 9=\frac{1}{|x|\sqrt{81x^2-1}}.$$ Thus, the answer is $\boxed{	ext{(B)}}$.

Find the derivative of the function f(x)=arcsec⁡(9x). \text { Find the derivative of the function } f ( x ) = \operatorname { arcsec } ( 9 x ) \text {. } Find the derivative of the function f(x)=arcsec(9x).

$\text { Find the derivative of the function } f ( x ) = \operatorname { arcsec } ( 9 x ) \text {. }$