Mister Exam

Derivative of ln(4x+5)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
log(4*x + 5)
$$\log{\left(4 x + 5 \right)}$$
d               
--(log(4*x + 5))
dx              
$$\frac{d}{d x} \log{\left(4 x + 5 \right)}$$
Detail solution
  1. Let .

  2. The derivative of is .

  3. Then, apply the chain rule. Multiply by :

    1. Differentiate term by term:

      1. The derivative of a constant times a function is the constant times the derivative of the function.

        1. Apply the power rule: goes to

        So, the result is:

      2. The derivative of the constant is zero.

      The result is:

    The result of the chain rule is:

  4. Now simplify:


The answer is:

The graph
The first derivative [src]
   4   
-------
4*x + 5
$$\frac{4}{4 x + 5}$$
The second derivative [src]
   -16    
----------
         2
(5 + 4*x) 
$$- \frac{16}{\left(4 x + 5\right)^{2}}$$
The third derivative [src]
   128    
----------
         3
(5 + 4*x) 
$$\frac{128}{\left(4 x + 5\right)^{3}}$$
The graph
Derivative of ln(4x+5)