Use logarithmic differentiation to find $\frac { \mathrm { d } y } { \mathrm {~d} x }$ . Do not simplify the result. $y = ( 5 x + 1 ) ( 7 x - 1 )$
A) $\frac { d y } { d x } = ( 5 x + 1 ) ( 7 x - 1 ) \left( \frac { 5 } { 5 x + 1 } + \frac { 7 } { 7 x - 1 } \right)$
B) $\frac { \mathrm { d } y } { \mathrm {~d} x } = \left( \frac { 5 } { 5 x + 1 } + \frac { 7 } { 7 x - 1 } \right)$
C) $\frac { \mathrm { d } y } { \mathrm {~d} x } = ( 5 x + 1 ) ( 7 x - 1 ) \left( \frac { 5 } { 5 x + 1 } + \frac { 7 } { 7 x - 1 } \right) ^ { 2 }$
D) $\frac { \mathrm { d } y } { \mathrm {~d} x } = ( 7 x - 1 ) \left( \frac { 5 } { 5 x + 1 } + \frac { 7 } { 7 x - 1 } \right)$
E) $\frac { \mathrm { d } y } { \mathrm {~d} x } = ( 5 x + 1 ) \left( \frac { 5 } { 5 x + 1 } + \frac { 7 } { 7 x - 1 } \right)$

Question

Use logarithmic differentiation to find $\frac { \mathrm { d } y } { \mathrm {~d} x }$ . Do not simplify the result.  $y = ( 5 x + 1 ) ( 7 x - 1 )$  
A) $\frac { d y } { d x } = ( 5 x + 1 ) ( 7 x - 1 ) \left( \frac { 5 } { 5 x + 1 } + \frac { 7 } { 7 x - 1 } \right)$
B)  $\frac { \mathrm { d } y } { \mathrm {~d} x } = \left( \frac { 5 } { 5 x + 1 } + \frac { 7 } { 7 x - 1 } \right)$
C) $\frac { \mathrm { d } y } { \mathrm {~d} x } = ( 5 x + 1 ) ( 7 x - 1 ) \left( \frac { 5 } { 5 x + 1 } + \frac { 7 } { 7 x - 1 } \right) ^ { 2 }$
D)   $\frac { \mathrm { d } y } { \mathrm {~d} x } = ( 7 x - 1 ) \left( \frac { 5 } { 5 x + 1 } + \frac { 7 } { 7 x - 1 } \right)$
E)  $\frac { \mathrm { d } y } { \mathrm {~d} x } = ( 5 x + 1 ) \left( \frac { 5 } { 5 x + 1 } + \frac { 7 } { 7 x - 1 } \right)$

Quizplus · Accepted Answer

Using logarithmic differentiation, the derivative of the product of two functions is the original function times the sum of the derivatives of the logarithms of each function. This matches choice A.

Use Logarithmic Differentiation to Find dy dx\frac { \mathrm { d } y } { \mathrm {~d} x } dxdy​

Use Logarithmic Differentiation to Find $\frac { \mathrm { d } y } { \mathrm {~d} x }$