Mister Exam

Derivative of 7ln(x+5)-7x+10

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
7*log(x + 5) - 7*x + 10
$$\left(- 7 x + 7 \log{\left(x + 5 \right)}\right) + 10$$
7*log(x + 5) - 7*x + 10
Detail solution
  1. Differentiate term by term:

    1. Differentiate term by term:

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

        1. Let .

        2. The derivative of is .

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

          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 of the chain rule is:

        So, the result is:

      2. 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:

      The result is:

    2. The derivative of the constant is zero.

    The result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
       7  
-7 + -----
     x + 5
$$-7 + \frac{7}{x + 5}$$
The second derivative [src]
  -7    
--------
       2
(5 + x) 
$$- \frac{7}{\left(x + 5\right)^{2}}$$
The third derivative [src]
   14   
--------
       3
(5 + x) 
$$\frac{14}{\left(x + 5\right)^{3}}$$
The graph
Derivative of 7ln(x+5)-7x+10