Mister Exam

Other calculators

y=logx(x+1)
The derivative of the function/ y=logx(x+1)

Derivative of y=logx(x+1)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
log(x)*(x + 1)
$$\left(x + 1\right) \log{\left(x \right)}$$ 
d                 
--(log(x)*(x + 1))
dx
$$\frac{d}{d x} \left(x + 1\right) \log{\left(x \right)}$$
Transform
Detail solution

  1. Apply the product rule:

    ; to find :

    1. The derivative of is .

    ; to find :

    1. Differentiate term by term:

      1. Apply the power rule: goes to

      2. The derivative of the constant is zero.

      The result is:

    The result is:

  2. Now simplify:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
x + 1         
----- + log(x)
  x
$$\log{\left(x \right)} + \frac{x + 1}{x}$$
Simplify
The second derivative [src] 
    1 + x
2 - -----
      x  
---------
    x
$$\frac{2 - \frac{x + 1}{x}}{x}$$
Simplify
The third derivative [src] 
     2*(1 + x)
-3 + ---------
         x    
--------------
       2      
      x
$$\frac{-3 + \frac{2 \left(x + 1\right)}{x}}{x^{2}}$$
Simplify
The graph
Derivative of y=logx(x+1)
    © Mister Exam – Calculator