Question

Finding Derivatives Implicity In Exercise, find dy/dx implicity. ln xy + 5x = 30

Answer 1

Answer:

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