Find dy/dx 8x^2-10xy+3y^2=26

Problem

8*x2−10*x*y+3*y2=26

Solution

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

(d(8)*x2)/d(x)−(d(10)*x*y)/d(x)+(d(3)*y2)/d(x)=d(26)/d(x)

2. Apply the product rule to the term −10*x*y and the power rule to the other terms.

16*x−(10*y+10*xd(y)/d(x))+6*yd(y)/d(x)=0

3. Distribute the negative sign and group the terms containing d(y)/d(x) on one side of the equation.

16*x−10*y−10*xd(y)/d(x)+6*yd(y)/d(x)=0

4. Factor out d(y)/d(x) from the relevant terms and move the remaining terms to the right side.

d(y)/d(x)*(6*y−10*x)=10*y−16*x

5. Solve for d(y)/d(x) by dividing both sides by the coefficient (6*y−10*x)

d(y)/d(x)=(10*y−16*x)/(6*y−10*x)

6. Simplify the fraction by dividing the numerator and denominator by their greatest common factor, which is 2

d(y)/d(x)=(5*y−8*x)/(3*y−5*x)

Final Answer

d(y)/d(x)=(5*y−8*x)/(3*y−5*x)

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