Solve the problem.
-$$\text { Evaluate } \frac { d w } { d t } \text { at } t = \frac { 1 } { 2 } \pi \text { for the function } w = x ^ { 2 } - y ^ { 2 } - 3 x ; x = \operatorname { cost } , y = \sin t$$
A) 3
B) -5
C) -7
D) -1

Question

Quizplus · Accepted Answer

Explanation:Given $$w = x ^ { 2 } - y ^ { 2 } - 3 x ; x = \operatorname { cost } , y = \sin t$$$$\frac { d w } { d t } = \frac { \partial w } { \partial x } \frac { d x } { d t } + \frac { \partial w } { \partial y } \frac { d y } { d t }$$$$\frac { d w } { d t } = (2x-3)(-\sin t) + (-2y)(\cos t)$$$$\frac { d w } { d t } = (-2\cos t -3)\sin t + 2\sin t \cos t$$$$\frac { d w } { d t } = -2\sin t \cos t -3\sin t + 2\sin t \cos t$$$$\frac { d w } { d t } = -3\sin t$$At $t = \frac { 1 } { 2 } \pi$,$$\frac { d w } { d t } = -3\sin \frac { 1 } { 2 } \pi = -3$$

Solve the Problem A) 3 B) -5 C) -7 D) -1

Solve the Problem A) 3
B) -5
C) -7
D) -1