$\text { Find the derivative of the function } y = \ln \sqrt { x ^ { 2 } - 7 } \text {. }$
A) $\frac { d y } { d x } = \frac { x } { 2 x - 7 }$
B) $\frac { d y } { d x } = \frac { 2 x } { \sqrt { x ^ { 2 } - 7 } }$
C) $\frac { d y } { d x } = \frac { 1 } { x ^ { 2 } - 7 }$
D) $\frac { d y } { d x } = \frac { x } { x ^ { 2 } - 7 }$
E) $\frac { d y } { d x } = \frac { 1 } { 2 x - 7 }$

Question

$\text { Find the derivative of the function } y = \ln \sqrt { x ^ { 2 } - 7 } \text {. }$ 
A) $\frac { d y } { d x } = \frac { x } { 2 x - 7 }$
B) $\frac { d y } { d x } = \frac { 2 x } { \sqrt { x ^ { 2 } - 7 } }$
C) $\frac { d y } { d x } = \frac { 1 } { x ^ { 2 } - 7 }$
D) $\frac { d y } { d x } = \frac { x } { x ^ { 2 } - 7 }$
E) $\frac { d y } { d x } = \frac { 1 } { 2 x - 7 }$

Quizplus · Accepted Answer

The derivative of $ y = \ln \sqrt{x^2 - 7} $ is found using the chain rule. Rewrite the function as $ y = \frac{1}{2} \ln(x^2 - 7) $. The derivative is $\frac{1}{2} \cdot \frac{1}{x^2 - 7} \cdot 2x = \frac{x}{x^2 - 7}$.

Find the derivative of the function y=ln⁡x2−7. \text { Find the derivative of the function } y = \ln \sqrt { x ^ { 2 } - 7 } \text {. } Find the derivative of the function y=lnx2−7​.

$\text { Find the derivative of the function } y = \ln \sqrt { x ^ { 2 } - 7 } \text {. }$