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The derivative of the function/ 4log2*x

Derivative of 4log2*x

The solution

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4*log(2*x)

$$4 \log{\left(2 x \right)}$$

d             
--(4*log(2*x))
dx

$$\frac{d}{d x} 4 \log{\left(2 x \right)}$$

Transform

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = 2 x$ .
2. The derivative of $\log{\left(u \right)}$ is $\frac{1}{u}$ .
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} 2 x$ :
  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: $2$
  The result of the chain rule is:
  
  $\frac{1}{x}$
So, the result is: $\frac{4}{x}$

The answer is:

$\frac{4}{x}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

4
-
x

$$\frac{4}{x}$$

Simplify

The second derivative [src]

-4 
---
  2
 x

$$- \frac{4}{x^{2}}$$

Simplify

The third derivative [src]

8 
--
 3
x

$$\frac{8}{x^{3}}$$

Simplify

The graph

Derivative of 4log2*x