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log(x)/log(3)-(1/x)

How to use it?
Derivative of:
Derivative of 2/e^x
Derivative of x^3*lnx
Derivative of x-ln(1+x)
Derivative of x*(1-x)
Identical expressions
log(x)/log(three)-(one /x)
logarithm of (x) divide by logarithm of (3) minus (1 divide by x)
logarithm of (x) divide by logarithm of (three) minus (one divide by x)
logx/log3-1/x
log(x) divide by log(3)-(1 divide by x)
Similar expressions
log(x)/log(3)+(1/x)

The derivative of the function/ log(x)/log(3)-(1/x)

Derivative of log(x)/log(3)-(1/x)

The solution

You have entered [src]

log(x)   1
------ - -
log(3)   x

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

log(x)/log(3) - 1/x

Detail solution

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

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

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

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

Simplify

The graph

Derivative of log(x)/log(3)-(1/x)