Find dy/dx y^2+3x=8

Problem

y2+3*x=8

Solution

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

d()/d(x)*(y2+3*x)=d(8)/d(x)

2. Apply the chain rule to the y2 term and the power rule to the 3*x term.

2*yd(y)/d(x)+3=0

3. Isolate the term containing d(y)/d(x) by subtracting 3 from both sides.

2*yd(y)/d(x)=−3

4. Solve for the derivative by dividing both sides by 2*y

d(y)/d(x)=−3/(2*y)

Final Answer

d(y)/d(x)=−3/(2*y)

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