Find $y ^ { \prime }$ . $y = \frac { 8 + \ln x } { x ^ { 6 } }$
A) $\frac { 6 \ln x + 47 } { x ^ { 5 } }$
B) $- \frac { 48 \ln x + 5 } { x ^ { 5 } }$
C) $- \frac { 6 \ln x + 47 } { x ^ { 7 } }$
D) $- \frac { 8 \ln x + 5 } { x ^ { 7 } }$
E) $\frac { 48 \ln x - 47 } { x ^ { 7 } }$

Question

Quizplus · Accepted Answer

To find the derivative of $y = \frac { 8 + \ln x } { x ^ { 6 } }$, use the quotient rule and the derivative of $\ln x$, which is $\frac{1}{x}$. The derivative is $\frac{d}{dx}\left(\frac { 8 + \ln x } { x ^ { 6 } }\right) = \frac{x^6 \cdot \frac{d}{dx}(8 + \ln x) - (8 + \ln x) \cdot \frac{d}{dx}(x^6)}{(x^6)^2}$. Simplifying, we get $\frac{x^6(1/x) - 6x^5(8 + \ln x)}{x^{12}} = \frac{1 - 6x(8 + \ln x)}{x^7} = - \frac { 6 \ln x + 47 } { x ^ { 7 } }$.

Find y′y ^ { \prime }y′ y=8+ln⁡xx6y = \frac { 8 + \ln x } { x ^ { 6 } }y=x68+lnx​

Find $y ^ { \prime }$ $y = \frac { 8 + \ln x } { x ^ { 6 } }$