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Derivative of:
Derivative of e^x^2
Derivative of tanh(x)
Derivative of cos²x
Derivative of (π-2x)³
Integral of d{x}:
(1-2*x)/x^2
Identical expressions
(one - two *x)/x^ two
(1 minus 2 multiply by x) divide by x squared
(one minus two multiply by x) divide by x to the power of two
(1-2*x)/x2
1-2*x/x2
(1-2*x)/x²
(1-2*x)/x to the power of 2
(1-2x)/x^2
(1-2x)/x2
1-2x/x2
1-2x/x^2
(1-2*x) divide by x^2
Similar expressions
(1+2*x)/x^2

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

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

The solution

You have entered [src]

1 - 2*x
-------
    2  
   x

$$\frac{1 - 2 x}{x^{2}}$$

(1 - 2*x)/x^2

Detail solution

Apply the quotient rule, which is:

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

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

To find $\frac{d}{d x} f{\left(x \right)}$ :
1. Differentiate $1 - 2 x$ 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. Apply the power rule: $x$ goes to $1$
    So, the result is: $-2$
  The result is: $-2$
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:

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

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

  /    3*(-1 + 2*x)\
2*|4 - ------------|
  \         x      /
--------------------
          3         
         x

$$\frac{2 \left(4 - \frac{3 \left(2 x - 1\right)}{x}\right)}{x^{3}}$$

Simplify

The third derivative [src]

   /     2*(-1 + 2*x)\
12*|-3 + ------------|
   \          x      /
----------------------
           4          
          x

$$\frac{12 \left(-3 + \frac{2 \left(2 x - 1\right)}{x}\right)}{x^{4}}$$

Simplify