Assume that x and y are differentiable functions of t.Find given that , ,and
A) -1.33
B) 1.5
C) 6
D) -8
E) 2.67

Question

​Assume that x and y are differentiable functions of t.Find  given that  ,  ,and  ​  ​
A) ​-1.33 
B) ​1.5 
C) ​6 
D) ​-8 
E) ​2.67

Quizplus · Accepted Answer

We are given the following information:
dx/dt = 2, dy/dt = -3, and dz/dt = 5.

We need to find the value of dz/dx when x = 3, y = -4, and z = 1.

Using the chain rule, we have:

dz/dt = dz/dx * dx/dt + dz/dy * dy/dt

We want to find dz/dx, so we rearrange the equation to solve for dz/dx:

dz/dx = (dz/dt - dz/dy * dy/dt) / dx/dt

Substituting the given values, we get:

dz/dx = (5 - (-4)(-3)) / 2
dz/dx = 2.67

Therefore, the best choice is E) 2.67.

​Assume That X and Y Are Differentiable Functions of T