Assume that x and y are differentiable functions of t. In each case, find given that , , and .
A) 11
B) 13
C) 22
D) 1
E) -22

Question

Assume that x and y are differentiable functions of t. In each case, find  given that  ,  , and  . ​  ​
A) 11 
B) 13 
C) 22 
D) 1 
E) -22

Quizplus · Accepted Answer

By the Chain Rule, we have
11ea984b_b1e2_c85b_9029_f7c77a4cb978_TB4005_11 = 11ea984b_b1e2_ef6d_9029_873f6dbf4739_TB4005_11 * (dy/dt) + 11ea984b_b1e2_ef6e_9029_25af9b9a519a_TB4005_11 * (dx/dt)
Substituting the given values, we get
(-1) = 8(dy/dt) + 6(dx/dt)
Solving for (dy/dt), we get
(dy/dt) = (-1 - 6(dx/dt))/8
Now, we are asked to find the value of (dy/dt) when dx/dt = -2. Substituting this value, we get
(dy/dt) = (-1 - 6(-2))/8 = (-1 + 12)/8 = 11/8
Therefore, the answer is A) 11.

Assume That X and Y Are Differentiable Functions of T