Question

Find dy/dx by implicit differentiation.
3x2 + 5xy − y2 = 5

Answer 1

\(3x^2+5xy-y^2=5\implies 6x+5(y+x*\frac{dy}{dx})-2y\frac{dy}{dx}=0\)

Answer 2

make sense so far?

Answer 3

that middle part is the product rule for \(xy\)

Answer 4

and that last part is the chain rule on \(y^2\)

Answer 5

so we have \(6x+5y+5x\frac{dy}{dx}-2y\frac{dy}{dx}=0\)
Now solve for \(\frac{dy}{dx}\)