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) $\frac{d w}{d x} \frac{\partial x}{\partial t}+\frac{d w}{d y} \frac{\partial y}{\partial t}$

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) $\frac{d w}{d x} \frac{\partial x}{\partial t}+\frac{d w}{d y} \frac{\partial y}{\partial t}$

1 Answer

127 votes

$\frac{\partial w}{\partial x} \frac{d x}{d t}+\frac{\partial w}{\partial y} \frac{d y}{d t}$

127 votes

127