Mister Exam

Other calculators

The derivative of the function/ f(x)=(x+1)^x-1

Derivative of f(x)=(x+1)^x-1

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
       x    
(x + 1)  - 1
(x+1)x−1\left(x + 1\right)^{x} - 1 
(x + 1)^x - 1
Detail solution

  1. Differentiate (x+1)x−1\left(x + 1\right)^{x} - 1 term by term:

    1. Don't know the steps in finding this derivative.

      But the derivative is

      xx(log⁡(x)+1)x^{x} \left(\log{\left(x \right)} + 1\right)

    2. The derivative of the constant −1-1 is zero.

    The result is: xx(log⁡(x)+1)x^{x} \left(\log{\left(x \right)} + 1\right)

The answer is:

xx(log⁡(x)+1)x^{x} \left(\log{\left(x \right)} + 1\right)

The graph
02468-8-6-4-2-1010-100000000000100000000000
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
       x /  x               \
(x + 1) *|----- + log(x + 1)|
         \x + 1             /
(x+1)x(xx+1+log⁡(x+1))\left(x + 1\right)^{x} \left(\frac{x}{x + 1} + \log{\left(x + 1 \right)}\right)
Simplify
The second derivative [src] 
         /                               x  \
         |                    2   -2 + -----|
       x |/  x               \         1 + x|
(1 + x) *||----- + log(1 + x)|  - ----------|
         \\1 + x             /      1 + x   /
(x+1)x((xx+1+log⁡(x+1))2−xx+1−2x+1)\left(x + 1\right)^{x} \left(\left(\frac{x}{x + 1} + \log{\left(x + 1 \right)}\right)^{2} - \frac{\frac{x}{x + 1} - 2}{x + 1}\right)
Simplify
The third derivative [src] 
         /                              2*x      /       x  \ /  x               \\
         |                    3   -3 + -----   3*|-2 + -----|*|----- + log(1 + x)||
       x |/  x               \         1 + x     \     1 + x/ \1 + x             /|
(1 + x) *||----- + log(1 + x)|  + ---------- - -----------------------------------|
         |\1 + x             /            2                   1 + x               |
         \                         (1 + x)                                        /
(x+1)x((xx+1+log⁡(x+1))3−3(xx+1−2)(xx+1+log⁡(x+1))x+1+2xx+1−3(x+1)2)\left(x + 1\right)^{x} \left(\left(\frac{x}{x + 1} + \log{\left(x + 1 \right)}\right)^{3} - \frac{3 \left(\frac{x}{x + 1} - 2\right) \left(\frac{x}{x + 1} + \log{\left(x + 1 \right)}\right)}{x + 1} + \frac{\frac{2 x}{x + 1} - 3}{\left(x + 1\right)^{2}}\right)
Simplify
    © Mister Exam – Calculator