Find dy/dx 4xy=32

Problem

4*x*y=32

Solution

1. Simplify the equation by dividing both sides by 4 to isolate the product of variables.

x*y=8

2. Apply implicit differentiation to both sides of the equation with respect to x

(d(x)*y)/d(x)=d(8)/d(x)

3. Use the product rule on the left side, where (d(u)*v)/d(x)=ud(v)/d(x)+vd(u)/d(x)

xd(y)/d(x)+yd(x)/d(x)=0

4. Simplify the derivative of x with respect to x which is 1.

xd(y)/d(x)+y=0

5. Isolate the term containing d(y)/d(x) by subtracting y from both sides.

xd(y)/d(x)=−y

6. Solve for d(y)/d(x) by dividing both sides by x

d(y)/d(x)=−y/x

Final Answer

d(y)/d(x)=−y/x

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