Finding derivatives implicity in exercise, find dy/dx implicity.
ln xy + 5x = 30

dy/dx = -5y - y/x

Step-by-step explanation:

In xy + 5x = 30

Differentiating xy implicitly

y + xdy/dx

Assuming u = xy

In xy = In u

Differentiating In u = 1/u = 1/xy

Differentiating 5x = 5 and differentiating a constant (30) = 0

1/xy(y + xdy/dx) + 5 = 0

(y + xdy/dx)/xy = -5

(y + xdy/dx) = -5xy

xdy/dx = -5xy - y

dy/dx = = (-5xy - y)/x

dy/dx = -5y - y/x

step-by-step explanation:

i found the koficent of the linear function and i foun c acordind to the strict formula y=kx+c and then i took 2 as an x and replacet it on the formula i found and then foun the y

b. y = 4x - 2

step-by-step explanation:

to find a parallel equation to an equation, make sure both equations have the same slope but different y-intercepts.

y = 4x + 1

4 = slope

1 = y-intercept

y = 4x - 2

4 = slope

-2 = y-intercept

they both have the same slope but different y-intercepts, so, b. is the correct answer.

and to check your work, you can graph both equations. : )