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

Problem

2*x3−3*y2=8

Solution

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

d()/d(x)*(2*x3−3*y2)=d(8)/d(x)

2. Apply the Power Rule to the x term and the Chain Rule to the y term.

6*x2−6*yd(y)/d(x)=0

3. Isolate the term containing d(y)/d(x) by subtracting 6*x2 from both sides.

−6*yd(y)/d(x)=−6*x2

4. Solve for dy/dx by dividing both sides by −6*y

d(y)/d(x)=(−6*x2)/(−6*y)

5. Simplify the fraction by canceling the common factor of −6

d(y)/d(x)=(x2)/y

Final Answer

d(y)/d(x)=(x2)/y

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