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Derivative of:
Derivative of -e^x
Derivative of 1/2*sqrt(x)
Derivative of x-7
Derivative of x^5-5*x^3-20*x
Identical expressions
(log(x)/log(two))- three (log(x)/log(three))
( logarithm of (x) divide by logarithm of (2)) minus 3( logarithm of (x) divide by logarithm of (3))
( logarithm of (x) divide by logarithm of (two)) minus three ( logarithm of (x) divide by logarithm of (three))
logx/log2-3logx/log3
(log(x) divide by log(2))-3(log(x) divide by log(3))
Similar expressions
(log(x)/log(2))+3(log(x)/log(3))

Derivative of (log(x)/log(2))-3(log(x)/log(3))

You have entered [src]

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

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

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

Detail solution

Differentiate $- 3 \frac{\log{\left(x \right)}}{\log{\left(3 \right)}} + \frac{\log{\left(x \right)}}{\log{\left(2 \right)}}$ term by term:
1. The derivative of a constant times a function is the constant times the derivative of the function.
  1. The derivative of $\log{\left(x \right)}$ is $\frac{1}{x}$ .
  So, the result is: $\frac{1}{x \log{\left(2 \right)}}$
2. 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. The derivative of $\log{\left(x \right)}$ is $\frac{1}{x}$ .
    So, the result is: $\frac{1}{x \log{\left(3 \right)}}$
  So, the result is: $- \frac{3}{x \log{\left(3 \right)}}$
The result is: $- \frac{3}{x \log{\left(3 \right)}} + \frac{1}{x \log{\left(2 \right)}}$
Now simplify:

$\frac{- \frac{3}{\log{\left(3 \right)}} + \frac{1}{\log{\left(2 \right)}}}{x}$

The answer is:

$\frac{- \frac{3}{\log{\left(3 \right)}} + \frac{1}{\log{\left(2 \right)}}}{x}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   1          3    
-------- - --------
x*log(2)   x*log(3)

$$- \frac{3}{x \log{\left(3 \right)}} + \frac{1}{x \log{\left(2 \right)}}$$

Simplify

The second derivative [src]

    1        3   
- ------ + ------
  log(2)   log(3)
-----------------
         2       
        x

$$\frac{- \frac{1}{\log{\left(2 \right)}} + \frac{3}{\log{\left(3 \right)}}}{x^{2}}$$

Simplify

The third derivative [src]

  /  1        3   \
2*|------ - ------|
  \log(2)   log(3)/
-------------------
          3        
         x

$$\frac{2 \left(- \frac{3}{\log{\left(3 \right)}} + \frac{1}{\log{\left(2 \right)}}\right)}{x^{3}}$$

Simplify