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Derivative of:
Derivative of arctg(1/x)
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Derivative of cot(1/x)
Identical expressions
log(eight *x)- eight *x+ seven
logarithm of (8 multiply by x) minus 8 multiply by x plus 7
logarithm of (eight multiply by x) minus eight multiply by x plus seven
log(8x)-8x+7
log8x-8x+7
Similar expressions
log(8*x)+8*x+7
log(8*x)-8*x-7

The derivative of the function/ log(8*x)-8*x+7

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

The solution

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

$$- 8 x + \log{\left(8 x \right)} + 7$$

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

$$\frac{d}{d x} \left(- 8 x + \log{\left(8 x \right)} + 7\right)$$

Transform

Detail solution

Differentiate $- 8 x + \log{\left(8 x \right)} + 7$ term by term:
1. Let $u = 8 x$ .
2. The derivative of $\log{\left(u \right)}$ is $\frac{1}{u}$ .
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} 8 x$ :
  1. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Apply the power rule: $x$ goes to $1$
    So, the result is: $8$
  The result of the chain rule is:
  
  $\frac{1}{x}$
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: $x$ goes to $1$
    So, the result is: $8$
  So, the result is: $-8$
5. The derivative of the constant $7$ is zero.
The result is: $-8 + \frac{1}{x}$

The answer is:

$-8 + \frac{1}{x}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

     1
-8 + -
     x

$$-8 + \frac{1}{x}$$

Simplify

The second derivative [src]

-1 
---
  2
 x

$$- \frac{1}{x^{2}}$$

Simplify

The third derivative [src]

2 
--
 3
x

$$\frac{2}{x^{3}}$$

Simplify

The graph

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