Mister Exam

Derivative of ln(x+2)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
log(x + 2)
log(x+2)\log{\left(x + 2 \right)}
log(x + 2)
Detail solution
  1. Let u=x+2u = x + 2.

  2. The derivative of log(u)\log{\left(u \right)} is 1u\frac{1}{u}.

  3. Then, apply the chain rule. Multiply by ddx(x+2)\frac{d}{d x} \left(x + 2\right):

    1. Differentiate x+2x + 2 term by term:

      1. Apply the power rule: xx goes to 11

      2. The derivative of the constant 22 is zero.

      The result is: 11

    The result of the chain rule is:

    1x+2\frac{1}{x + 2}

  4. Now simplify:

    1x+2\frac{1}{x + 2}


The answer is:

1x+2\frac{1}{x + 2}

The graph
02468-8-6-4-2-1010-2525
The first derivative [src]
  1  
-----
x + 2
1x+2\frac{1}{x + 2}
The second derivative [src]
  -1    
--------
       2
(2 + x) 
1(x+2)2- \frac{1}{\left(x + 2\right)^{2}}
The third derivative [src]
   2    
--------
       3
(2 + x) 
2(x+2)3\frac{2}{\left(x + 2\right)^{3}}
The graph
Derivative of ln(x+2)