Compute the indicated derivative using the chain rule. $y = 10 x ^ { 2 } - 7 x ; \left. \frac { \mathrm { d } x } { \mathrm {~d} y } \right| _ { x = 2 }$
A) $\frac { 1 } { 33 }$
B) $\frac { 7 } { 10 }$
C) $\frac { 1 } { 13 }$
D) 2
E) $\frac { 10 } { 7 }$

Question

Compute the indicated derivative using the chain rule.   $y = 10 x ^ { 2 } - 7 x ; \left. \frac { \mathrm { d } x } { \mathrm {~d} y } \right| _ { x = 2 }$  
A) $\frac { 1 } { 33 }$
B) $\frac { 7 } { 10 }$
C) $\frac { 1 } { 13 }$
D) 2
E) $\frac { 10 } { 7 }$

Quizplus · Accepted Answer

The derivative of $y$ with respect to $x$ is $dy/dx = 20x - 7$. To find $dx/dy$, take the reciprocal of $dy/dx$. At $x = 2$, $dy/dx = 20(2) - 7 = 40 - 7 = 33$, so $dx/dy = 1/33$.

Compute the Indicated Derivative Using the Chain Rule y=10x2−7x;dx dy∣x=2y = 10 x ^ { 2 } - 7 x ; \left. \frac { \mathrm { d } x } { \mathrm {~d} y } \right| _ { x = 2 }y=10x2−7x; dydx​​x=2​

Compute the Indicated Derivative Using the Chain Rule $y = 10 x ^ { 2 } - 7 x ; \left. \frac { \mathrm { d } x } { \mathrm {~d} y } \right| _ { x = 2 }$