Let $w=f(x, y),$ where $x$ and $y$ are functions of $t .$ Then, according to the chain rule, $\frac{d w}{d t}$ is equal to
(A) $\frac{d w}{d x} \frac{d x}{d t}+\frac{d w}{d y} \frac{d t}{d t}$
(B) $\frac{\partial w}{\partial x} \frac{\partial x}{\partial t}+\frac{\partial w}{\partial y} \frac{\partial y}{\partial t}$
(C) $\frac{\partial w}{\partial x} \frac{d x}{d t}+\frac{\partial w}{\partial y} \frac{d y}{d t}$
(D) $\frac{d w}{d x} \frac{\partial x}{\partial t}+\frac{d w}{d y} \frac{\partial y}{\partial t}$

Question ID - 156690 | SaraNextGen Top Answer

Let $w=f(x, y),$ where $x$ and $y$ are functions of $t .$ Then, according to the chain rule, $\frac{d w}{d t}$ is equal to
(A) $\frac{d w}{d x} \frac{d x}{d t}+\frac{d w}{d y} \frac{d t}{d t}$
(B) $\frac{\partial w}{\partial x} \frac{\partial x}{\partial t}+\frac{\partial w}{\partial y} \frac{\partial y}{\partial t}$
(C) $\frac{\partial w}{\partial x} \frac{d x}{d t}+\frac{\partial w}{\partial y} \frac{d y}{d t}$
(D) $\frac{d w}{d x} \frac{\partial x}{\partial t}+\frac{d w}{d y} \frac{\partial y}{\partial t}$