Find dy/dx x^2y+2x^3y=x+y

Problem

x2*y+2*x3*y=x+y

Solution

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

d()/d(x)*(x2*y+2*x3*y)=d()/d(x)*(x+y)

2. Apply the product rule to the terms on the left side.

(2*x*y+x2d(y)/d(x))+(6*x2*y+2*x3d(y)/d(x))=1+d(y)/d(x)

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

x2d(y)/d(x)+2*x3d(y)/d(x)−d(y)/d(x)=1−2*x*y−6*x2*y

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

d(y)/d(x)*(x2+2*x3−1)=1−2*x*y−6*x2*y

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

d(y)/d(x)=(1−2*x*y−6*x2*y)/(x2+2*x3−1)

Final Answer

d(y)/d(x)=(1−2*x*y−6*x2*y)/(x2+2*x3−1)

Want more problems? Check here!