Find dy/dx xy^2=4

Problem

x*y2=4

Solution

1. Differentiate both sides with respect to x using implicit differentiation.

(d(x)*y2)/d(x)=d(4)/d(x)

2. Apply the product rule to the left side, where the derivative of x*y2 is x⋅d(y2)/d(x)+y2⋅d(x)/d(x)

x⋅d(y2)/d(x)+y2⋅1=0

3. Apply the chain rule to differentiate y2 with respect to x treating y as a function of x

x⋅2*yd(y)/d(x)+y2=0

4. Isolate the term containing d(y)/d(x) by subtracting y2 from both sides.

2*x*yd(y)/d(x)=−y2

5. Solve for dy/dx by dividing both sides by 2*x*y

d(y)/d(x)=(−y2)/(2*x*y)

6. Simplify the expression by canceling the common factor of y in the numerator and denominator.

d(y)/d(x)=−y/(2*x)

Final Answer

d(y)/d(x)=−y/(2*x)

Want more problems? Check here!