Find dy/dx -7xy+3y-7=0

Problem

−7*x*y+3*y−7=0

Solution

1. Differentiate both sides of the equation with respect to x treating y as a function of x and applying the product rule to the term −7*x*y

d()/d(x)*(−7*x*y+3*y−7)=d()/d(x)*0

2. Apply the product rule to −7*x*y which gives −7*y−7*xd(y)/d(x) and differentiate the remaining terms.

−7*y−7*xd(y)/d(x)+3d(y)/d(x)=0

3. Isolate the terms containing d(y)/d(x) on one side of the equation by moving −7*y to the right side.

−7*xd(y)/d(x)+3d(y)/d(x)=7*y

4. Factor out d(y)/d(x) from the terms on the left side.

d(y)/d(x)*(−7*x+3)=7*y

5. Solve for d(y)/d(x) by dividing both sides by (−7*x+3)

d(y)/d(x)=(7*y)/(3−7*x)

Final Answer

d(y)/d(x)=(7*y)/(3−7*x)

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