Use implicit differentiation to find the derivative y' of the following: Wrote the solution of each number

Question

6.y²e^2x + xy³ - 1=0

ans. y' =y² + 2ye^2x/ 2e^2x + 3xy

Answer 1

y²e^2x + xy³ -1 = 0

Take d/dx of each term in position. Use product rule and dx/dx = 1, dy/dx or y' is included in chain rule because y= y(x)

(2yy'e^2x + y²(2e^2x)) + (y³ + x(3y²y') +0 = 0

Group y' terms:

(2ye^2x + 3xy²)y' = -2y²e^2x - y³

The answer should be -(2y²e^2x - y³)/(2ye^2x + 3xy²)

The negative sign cannot be avoided, and you need to have the parentheses in place.