Find the equation of the tangent line for $( x y ) ^ { 2 } + ( x y ) - x = 10$ at the point $( - 10,0 )$ .
A) $y = - 10 x - 1$
B) $y = - \frac { 1 } { 10 } x + 1$
C) $y = - \frac { 1 } { 10 } x - 1$
D) $y = - 10 x - 2$
E) $y = - \frac { 1 } { 10 } x - 2$

Question

Find the equation of the tangent line for $( x y ) ^ { 2 } + ( x y ) - x = 10$ at the point $( - 10,0 )$ .  
A) $y = - 10 x - 1$
B)  $y = - \frac { 1 } { 10 } x + 1$
C)   $y = - \frac { 1 } { 10 } x - 1$
D)   $y = - 10 x - 2$
E)   $y = - \frac { 1 } { 10 } x - 2$

Quizplus · Accepted Answer

To find the tangent line, first implicitly differentiate the given equation with respect to $x$, then substitute the point $(-10, 0)$ to find the slope. The equation of the tangent line is then determined using the point-slope form.

Find the Equation of the Tangent Line For (xy)2+(xy)−x=10( x y ) ^ { 2 } + ( x y ) - x = 10(xy)2+(xy)−x=10

Find the Equation of the Tangent Line For $( x y ) ^ { 2 } + ( x y ) - x = 10$