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The derivative of the function/ 1/x-6x^2

You entered:

1/x-6x^2

What you mean?

1/(x - 6*x^2)

1*2/(x - 6*x)

1/(x - 6*x)^2

1*x^2/(x - 1*6)

1/x - 6*x^2

1/x - 6*x^2

Derivative of 1/x-6x^2

The solution

You have entered [src]

  1      2
1*- - 6*x 
  x

$$- 6 x^{2} + 1 \cdot \frac{1}{x}$$

d /  1      2\
--|1*- - 6*x |
dx\  x       /

$$\frac{d}{d x} \left(- 6 x^{2} + 1 \cdot \frac{1}{x}\right)$$

Transform

Detail solution

Differentiate $- 6 x^{2} + 1 \cdot \frac{1}{x}$ term by term:
1. Apply the quotient rule, which is:
  
  $\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}$
  
  $f{\left(x \right)} = 1$ and $g{\left(x \right)} = x$ .
  
  To find $\frac{d}{d x} f{\left(x \right)}$ :
  1. The derivative of the constant $1$ is zero.
  To find $\frac{d}{d x} g{\left(x \right)}$ :
  1. Apply the power rule: $x$ goes to $1$
  Now plug in to the quotient rule:
  
  $- \frac{1}{x^{2}}$
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. Apply the power rule: $x^{2}$ goes to $2 x$
    So, the result is: $12 x$
  So, the result is: $- 12 x$
The result is: $- 12 x - \frac{1}{x^{2}}$

The answer is:

$- 12 x - \frac{1}{x^{2}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

  1        
- -- - 12*x
   2       
  x

$$- 12 x - \frac{1}{x^{2}}$$

Simplify

The second derivative [src]

  /     1 \
2*|-6 + --|
  |      3|
  \     x /

$$2 \left(-6 + \frac{1}{x^{3}}\right)$$

Simplify

The third derivative [src]

-6 
---
  4
 x

$$- \frac{6}{x^{4}}$$

Simplify

The graph

Derivative of 1/x-6x^2