Use implicit and/or logarithmic differentiation to find the derivative y' of: Write the solution of each number

Question

9. x = ln(x+y+1)

ans. y' = x + y

Answer 1

Differentiation of x = ln(x+y+1) gives

1 = [1/(x + y + 1)] × (1 + y') = (1 + y')/(x + y + 1)

which means that

1 + y' = x + y + 1

which means that

y' = x + y