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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
Integral of d{x}:
(1-log(x))/x^2
Limit of the function:
(1-log(x))/x^2
Identical expressions
(one -log(x))/x^ two
(1 minus logarithm of (x)) divide by x squared
(one minus logarithm of (x)) divide by x to the power of two
(1-log(x))/x2
1-logx/x2
(1-log(x))/x²
(1-log(x))/x to the power of 2
1-logx/x^2
(1-log(x)) divide by x^2
Similar expressions
(1+log(x))/x^2

The derivative of the function/ (1-log(x))/x^2

Derivative of (1-log(x))/x^2

The solution

You have entered [src]

1 - log(x)
----------
     2    
    x

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

(1 - log(x))/x^2

Detail solution

Apply the quotient rule, which is:

$\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}$

$f{\left(x \right)} = 1 - \log{\left(x \right)}$ and $g{\left(x \right)} = x^{2}$ .

To find $\frac{d}{d x} f{\left(x \right)}$ :
1. Differentiate $1 - \log{\left(x \right)}$ term by term:
  1. The derivative of the constant $1$ is zero.
  2. 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: $- \frac{1}{x}$
  The result is: $- \frac{1}{x}$
To find $\frac{d}{d x} g{\left(x \right)}$ :
1. Apply the power rule: $x^{2}$ goes to $2 x$
Now plug in to the quotient rule:

$\frac{- 2 x \left(1 - \log{\left(x \right)}\right) - x}{x^{4}}$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

11 - 6*log(x)
-------------
       4     
      x

$$\frac{11 - 6 \log{\left(x \right)}}{x^{4}}$$

Simplify

The third derivative [src]

2*(-25 + 12*log(x))
-------------------
          5        
         x

$$\frac{2 \left(12 \log{\left(x \right)} - 25\right)}{x^{5}}$$

Simplify

The graph

Derivative of (1-log(x))/x^2