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

Multiple Choice

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) $\frac { \mathrm { d } y } { \mathrm {~d} x } = ( 5 x + 1 ) \left( \frac { 5 } { 5 x + 1 } + \frac { 7 } { 7 x - 1 } \right)$