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

question 97

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

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