Question

Find the derivative of (x + 1) ^ x

Answer 1

Answer:

Step-by-step explanation:

Let y = $(x + 1) ^{x}$

taking log on both sides,

log y = log $(x + 1) ^{x}$

log y = x log (x + 1)

Differentiating both sides,

1/y * dy/dx = x*1/(x+1) + log(x + 1).1

dy/dx = y(x/(x+1) + log(x + 1))

dy/dx = $(x + 1) ^{x}$($\frac{x}{(x + 1)}$ + log(x + 1))