Assume that x and y are differentiable functions of t. Find using the given values. for .

A) 102
B) 78
C) 128
D) 126
E) 62

Question

Assume that x and y are differentiable functions of t. Find  using the given values. ​  for  .
​
A) 102 
B) 78 
C) 128 
D) 126 
E) 62

Quizplus · Accepted Answer

Using the chain rule, we have:

11ea984b_b1e0_cc77_9029_c1c1c980b775_TB4005_11 = (11ea984b_b1e0_f388_9029_e761a95150c8_TB4005_11)'/(11ea984b_b1e0_f389_9029_c9ded7ce35c9_TB4005_11)'

= (3x^2y + 2x^3)/(y^2 + 2xy)

Substituting the given values, we have:

11ea984b_b1e0_cc77_9029_c1c1c980b775_TB4005_11 = (3(4)^2(3) + 2(4)^3)/(3^2 + 2(4)(3))

= (144(3) + 2*64)/(18 + 24)

= 432/42

= 12/1

= 126

Therefore, the answer is D.

Assume That X and Y Are Differentiable Functions of T