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

Question

Quizplus · Accepted Answer

The derivative of $y = \ln \sqrt{x^2 - 7}$ is found using the chain rule: $ \frac{d}{dx}(\ln u) = \frac{1}{u} \cdot \frac{du}{dx} $. Here, $ u = \sqrt{x^2 - 7} $, so $ \frac{du}{dx} = \frac{x}{\sqrt{x^2 - 7}} $. Thus, the derivative is $ \frac{1}{\sqrt{x^2 - 7}} \cdot \frac{x}{\sqrt{x^2 - 7}} = \frac{x}{x^2 - 7} $.

Find the Derivative of the Function y=ln⁡x2−7y = \ln \sqrt { x ^ { 2 } - 7 }y=lnx2−7​

Find the Derivative of the Function $y = \ln \sqrt { x ^ { 2 } - 7 }$