Find dy/dx 6x^2+8xy+4y^2+17y-6=0

Problem

6*x2+8*x*y+4*y2+17*y−6=0

Solution

1. Differentiate both sides of the equation with respect to x treating y as a function of x and applying the chain rule.

(d(6)*x2)/d(x)+(d(8)*x*y)/d(x)+(d(4)*y2)/d(x)+(d(17)*y)/d(x)−d(6)/d(x)=0

2. Apply the product rule to the term 8*x*y and the chain rule to terms involving y

12*x+(8*y+8*xd(y)/d(x))+8*yd(y)/d(x)+17d(y)/d(x)=0

3. Group all terms containing d(y)/d(x) on one side of the equation and move all other terms to the opposite side.

8*xd(y)/d(x)+8*yd(y)/d(x)+17d(y)/d(x)=−12*x−8*y

4. Factor out the common term d(y)/d(x) from the left side.

d(y)/d(x)*(8*x+8*y+17)=−12*x−8*y

5. Solve for d(y)/d(x) by dividing both sides by the expression in the parentheses.

d(y)/d(x)=(−12*x−8*y)/(8*x+8*y+17)

Final Answer

d(y)/d(x)=−(12*x+8*y)/(8*x+8*y+17)

Want more problems? Check here!