$\text { Find } \frac { d w } { d t } \text { using the appropriate Chain Rule for } w = x ^ { 2 } + y ^ { 2 } \text { where } x = 7 t \text { and } y = 3 t \text {. }$
A)116t
B)58t
C)104t
D)32t
E)174t

Question

Quizplus · Accepted Answer

Using the Chain Rule, we have:$$\frac{dw}{dt} = \frac{\partial w}{\partial x} \frac{dx}{dt} + \frac{\partial w}{\partial y} \frac{dy}{dt}$$where$$\frac{\partial w}{\partial x} = 2x \quad 	ext{ and } \quad \frac{\partial w}{\partial y} = 2y$$Substituting these partial derivatives and the given values of $x$ and $y$, we get:$$\frac{dw}{dt} = 2(7t)(7) + 2(3t)(3) = 98t + 18t = 116t$$Therefore, the correct choice is A.

A)116t B)58t C)104t D)32t E)174t

A)116t
B)58t
C)104t
D)32t
E)174t