Find dy/dx y+16xy-12=0

Problem

y+16*x*y−12=0

Solution

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

d(y)/d(x)+(d(16)*x*y)/d(x)−d(12)/d(x)=d(0)/d(x)

2. Apply the product rule to the term 16*x*y where the derivative is 16*y+16*xd(y)/d(x)

d(y)/d(x)+16*y+16*xd(y)/d(x)−0=0

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

d(y)/d(x)+16*xd(y)/d(x)=−16*y

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

d(y)/d(x)*(1+16*x)=−16*y

5. Solve for d(y)/d(x) by dividing both sides by (1+16*x)

d(y)/d(x)=(−16*y)/(1+16*x)

Final Answer

d(y)/d(x)=−(16*y)/(1+16*x)

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