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The derivative of the function/ y=log2x-3log3x

Derivative of y=log2x-3log3x

The solution

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log(2*x) - 3*log(3*x)

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

d                        
--(log(2*x) - 3*log(3*x))
dx

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

Transform

Detail solution

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

The answer is:

$- \frac{2}{x}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-2 
---
 x

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

Simplify

The second derivative [src]

2 
--
 2
x

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

Simplify

The third derivative [src]

-4 
---
  3
 x

$$- \frac{4}{x^{3}}$$

Simplify

The graph

Derivative of y=log2x-3log3x