Assume that x, y, and z are differentiable functions of t. If find when , , , and . Round your answer to two decimal places.
A) 14.25
B) 8.25
C) -1.75
D) 10.75
E) 1.63

Question

Assume that x, y, and z are differentiable functions of t. If  find  when  ,  ,  ,  and  . Round your answer to two decimal places.
A) 14.25 
B) 8.25 
C) -1.75 
D) 10.75 
E) 1.63

Quizplus · Accepted Answer

Using the Chain Rule, we can differentiate the given expression with respect to t:
$\frac{d}{dt}(x^2+y^2+z^2)=2x\frac{dx}{dt}+2y\frac{dy}{dt}+2z\frac{dz}{dt}$
We are given values for $x$, $y$, $z$, $\frac{dx}{dt}$, $\frac{dy}{dt}$, and $\frac{dz}{dt}$ at a particular point in time, so we can plug them in to get the answer:
$2(5)(-0.5)+2(3)(0.75)+2(-2)(1)=\boxed{8.25}$

Assume That X, Y, and Z Are Differentiable Functions of T