Find $\frac { d y } { d x }$ for the equation $\frac { x + 4 y } { 5 x - 6 y } = 6$ .
A) $\frac { d ^ { 2 } y } { d x } = - \frac { 29 } { 40 }$
B) $\frac { d y } { d x } = \frac { 31 } { 40 }$
C) $\frac { d y } { d x } = \frac { 29 } { 40 }$
D) $\frac { d ^ { 2 } y } { d x } = - \frac { 31 } { 40 }$
E) $\frac { d y } { d x } = 6$

Question

Quizplus · Accepted Answer

To find $\frac{dy}{dx}$, we first simplify the given equation: $\frac{x + 4y}{5x - 6y} = 6$. Cross-multiplying gives $x + 4y = 6(5x - 6y)$, which simplifies to $x + 4y = 30x - 36y$, or $29x = 40y$. Differentiating both sides with respect to $x$ gives $29 = 40\frac{dy}{dx}$, leading to $\frac{dy}{dx} = \frac{29}{40}$.

Find dydx\frac { d y } { d x }dxdy​ For the Equation

Find $\frac { d y } { d x }$ For the Equation