Assume that x and y are both differentiable functions of t . Find $\frac { d y } { d t }$ when $x = 49$ and $\frac { d x } { d t } = 17$ for the equation $y = \sqrt { x }$.
A) $\frac { d y } { d t } = \frac { 17 } { 14 }$
B) $\frac { d y } { d t } = 14$
C) $\frac { d y } { d t } = \frac { 14 } { 17 }$
D) $\frac { d y } { d t } = - \frac { 17 } { 14 }$
E) $\frac { d y } { d t } = - 14$

Question

Quizplus · Accepted Answer

By the chain rule, we have $\frac { d y } { d t } = \frac { d y } { d x } \cdot \frac { d x } { d t }$. Since $y = \sqrt{x}$, we have $\frac { d y } { d x } = \frac{1}{2\sqrt{x}}$. When $x=49$, we have $\frac { d y } { d x } = \frac{1}{14}$. Therefore, $\frac { d y } { d t } = \frac { d y } { d x } \cdot \frac { d x } { d t } = \frac {1}{14} \cdot 17 = \frac{17}{14}$. Hence the answer is $	extbf{(A)}$.

Assume That X and Y Are Both Differentiable Functions of T