$\text { Evaluate } \frac { d y } { d x } \text { for the equation } 7 x y = 21 \text { at the given point } ( - 3 , - 1 ) \text {. Round your }$ answer to two decimal places.
A) $\frac { d y } { d x } = 7.00$
B) $\frac { d y } { d x } = 63.00$
C) $\frac { d y } { d x } = - 0.33$
D) $\frac { d y } { d x } = - 63.00$
E) $\frac { d y } { d x } = - 3.00$

Question

Quizplus · Accepted Answer

To find $\frac{dy}{dx}$, we differentiate both sides of the equation $7xy = 21$ with respect to $x$. Using the product rule for differentiation, we get $7x\frac{dy}{dx} + 7y = 0$. Solving for $\frac{dy}{dx}$ gives $\frac{dy}{dx} = -\frac{7y}{7x} = -\frac{y}{x}$. Substituting $x = -3$ and $y = -1$ into this expression yields $\frac{dy}{dx} = -\frac{-1}{-3} = -\frac{1}{3} = -0.33$.