Calculate $\frac { \mathrm { d } y } { \mathrm {~d} x }$ . You need not expand your answer. $y = \left( \frac { x } { 1.2 } + \frac { 1.2 } { x } \right) \left( x ^ { 2 } + 7 \right)$
A) $2 x \left( \frac { 1 } { 1.2 } - \frac { 1.2 } { x ^ { 2 } } \right)$
B) $\left( \frac { 1 } { 1.2 } - \frac { 1.2 } { x ^ { 2 } } \right) \left( x ^ { 2 } + 7 \right) - 2 x \left( \frac { x } { 1.2 } + \frac { 1.2 } { x } \right)$
C) $2 x \left( \frac { 1 } { 1.2 } - \frac { 1.2 } { x ^ { 2 } } \right) + \left( \frac { x } { 1.2 } + \frac { 1.2 } { x } \right) \left( x ^ { 2 } + 7 \right)$
D) $2 x$
E) $\left( \frac { 1 } { 1.2 } - \frac { 1.2 } { x ^ { 2 } } \right) \left( x ^ { 2 } + 7 \right) + 2 x \left( \frac { x } { 1.2 } + \frac { 1.2 } { x } \right)$

Question

Calculate $\frac { \mathrm { d } y } { \mathrm {~d} x }$ . You need not expand your answer.   $y = \left( \frac { x } { 1.2 } + \frac { 1.2 } { x } \right) \left( x ^ { 2 } + 7 \right)$  
A) $2 x \left( \frac { 1 } { 1.2 } - \frac { 1.2 } { x ^ { 2 } } \right)$
B) $\left( \frac { 1 } { 1.2 } - \frac { 1.2 } { x ^ { 2 } } \right) \left( x ^ { 2 } + 7 \right) - 2 x \left( \frac { x } { 1.2 } + \frac { 1.2 } { x } \right)$
C) $2 x \left( \frac { 1 } { 1.2 } - \frac { 1.2 } { x ^ { 2 } } \right) + \left( \frac { x } { 1.2 } + \frac { 1.2 } { x } \right) \left( x ^ { 2 } + 7 \right)$
D) $2 x$
E) $\left( \frac { 1 } { 1.2 } - \frac { 1.2 } { x ^ { 2 } } \right) \left( x ^ { 2 } + 7 \right) + 2 x \left( \frac { x } { 1.2 } + \frac { 1.2 } { x } \right)$

Quizplus · Accepted Answer

To find the derivative of $y$, we apply the product rule: $(f \cdot g)' = f' \cdot g + f \cdot g'$. Here, $f = \frac{x}{1.2} + \frac{1.2}{x}$ and $g = x^2 + 7$. The derivative of $f$ is $\frac{1}{1.2} - \frac{1.2}{x^2}$ and the derivative of $g$ is $2x$. Substituting these into the product rule formula gives the expression in choice E.

Calculate dy dx\frac { \mathrm { d } y } { \mathrm {~d} x } dxdy​

Calculate $\frac { \mathrm { d } y } { \mathrm {~d} x }$