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log(8*x)-8*x+7

Derivative of log(8*x)-8*x+7

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
log(8*x) - 8*x + 7
$$- 8 x + \log{\left(8 x \right)} + 7$$
d                     
--(log(8*x) - 8*x + 7)
dx                    
$$\frac{d}{d x} \left(- 8 x + \log{\left(8 x \right)} + 7\right)$$
Detail solution
  1. Differentiate term by term:

    1. Let .

    2. The derivative of is .

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

      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:

      The result of the chain rule is:

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

      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:

      So, the result is:

    5. The derivative of the constant is zero.

    The result is:


The answer is:

The graph
The first derivative [src]
     1
-8 + -
     x
$$-8 + \frac{1}{x}$$
The second derivative [src]
-1 
---
  2
 x 
$$- \frac{1}{x^{2}}$$
The third derivative [src]
2 
--
 3
x 
$$\frac{2}{x^{3}}$$
The graph
Derivative of log(8*x)-8*x+7