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The derivative of the function/ 3log2x-e^2

Derivative of 3log2x-e^2

The solution

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              2
3*log(2*x) - e

$$3 \log{\left(2 x \right)} - e^{2}$$

d /              2\
--\3*log(2*x) - e /
dx

$$\frac{d}{d x} \left(3 \log{\left(2 x \right)} - e^{2}\right)$$

Transform

Detail solution

Differentiate $3 \log{\left(2 x \right)} - e^{2}$ term by term:
1. 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: $\frac{3}{x}$
2. The derivative of the constant $- e^{2}$ is zero.
The result is: $\frac{3}{x}$

The answer is:

$\frac{3}{x}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

3
-
x

$$\frac{3}{x}$$

Simplify

The second derivative [src]

-3 
---
  2
 x

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

Simplify

The third derivative [src]

6 
--
 3
x

$$\frac{6}{x^{3}}$$

Simplify

The graph

Derivative of 3log2x-e^2