Related Rates Calculus Question

Question

if y^2 + xy - 3x = 14, and dy/dt = -4 when x = -2 and y = -2, what is dx/dt when x= -2 and y= -2

Answer 1

Hi,

y^2 + xy - 3x = 14, 

First, you need to know:

(y²)' = 2yy'

(xy)' = x'y + y'x ( rule of product)

(3x)' = 3x'

Second, derivative of y^2 + xy - 3x = 14 ======> 2yy' + x'y + y'x - 3x' = 0 I

Third, replace given information to the equation # I

y'=dy/dt = -4 when x = -2 and y = -2

2(-2)(-4) + x' (-2) + (-4)(-2) - 3x'=0 ======> dx/dt = x' = 24/5

I hope it is useful,

Minoo