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

Question

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

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

ans. y' = x + y

Answer 1

An alternate way, same answer

x = ln(x+y+1)

Take e to the power of both sides

e^x= e^ln(x+y+1) = x+y+1

Doing implicit derivation

e^x=1+y'

y'=e^x-1

y'=e^ln(x+y+1)-1

y'=x+y+1-1 = x+y

Answer 2

x = ln(x + y + 1); 1 = (1 + y')/(x + y + 1); x + y + 1 = 1 + y'; y' = x + y