Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of x^(4/3)
Derivative of x*2^x
Derivative of (x^2)/36
Derivative of x+log(x)
Sum of series:
f(x)
Integral of d{x}:
f(x)
f(x)
Identical expressions
f(x)=(x+ one)^x- one
f(x) equally (x plus 1) to the power of x minus 1
f(x) equally (x plus one) to the power of x minus one
f(x)=(x+1)x-1
fx=x+1x-1
fx=x+1^x-1
Similar expressions
f(x)=(x+1)^x+1
f(x)=(x-1)^x-1

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

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

The solution

You have entered [src]

       x    
(x + 1)  - 1

$$\left(x + 1\right)^{x} - 1$$

(x + 1)^x - 1

Detail solution

Differentiate $\left(x + 1\right)^{x} - 1$ term by term:
1. Don't know the steps in finding this derivative.
  
  But the derivative is
  
  $x^{x} \left(\log{\left(x \right)} + 1\right)$
2. The derivative of the constant $-1$ is zero.
The result is: $x^{x} \left(\log{\left(x \right)} + 1\right)$

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

       x /  x               \
(x + 1) *|----- + log(x + 1)|
         \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   /

$$\left(x + 1\right)^{x} \left(\left(\frac{x}{x + 1} + \log{\left(x + 1 \right)}\right)^{2} - \frac{\frac{x}{x + 1} - 2}{x + 1}\right)$$

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)                                        /

$$\left(x + 1\right)^{x} \left(\left(\frac{x}{x + 1} + \log{\left(x + 1 \right)}\right)^{3} - \frac{3 \left(\frac{x}{x + 1} - 2\right) \left(\frac{x}{x + 1} + \log{\left(x + 1 \right)}\right)}{x + 1} + \frac{\frac{2 x}{x + 1} - 3}{\left(x + 1\right)^{2}}\right)$$

Simplify

Other calculators

How to use it?

Identical expressions

Similar expressions

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

The graph:

Piecewise:

The solution