Find dy/dx x^2y^3-2xy=6x+y+1

Problem

x2*y3−2*x*y=6*x+y+1

Solution

1. Differentiate both sides with respect to x treating y as a function of x and applying the product rule where necessary.

d()/d(x)*(x2*y3−2*x*y)=d()/d(x)*(6*x+y+1)

2. Apply the product rule to the terms x2*y3 and 2*x*y remembering to multiply by d(y)/d(x) whenever differentiating a y term.

(2*x*y3+x2⋅3*y2d(y)/d(x))−(2*y+2*xd(y)/d(x))=6+d(y)/d(x)

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

3*x2*y2d(y)/d(x)−2*xd(y)/d(x)−d(y)/d(x)=6−2*x*y3+2*y

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

d(y)/d(x)*(3*x2*y2−2*x−1)=6−2*x*y3+2*y

5. Solve for the derivative by dividing both sides by the expression in the parentheses.

d(y)/d(x)=(6−2*x*y3+2*y)/(3*x2*y2−2*x−1)

Final Answer

d(y)/d(x)=(6−2*x*y3+2*y)/(3*x2*y2−2*x−1)

Want more problems? Check here!