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Derivative of:
Derivative of (x^2-2)*(x^7+4)
Derivative of x*ln(x)
Derivative of x^2sinx
Derivative of x-sqrt(x)
Identical expressions
lgx- two *lg^2x
lgx minus 2 multiply by lg squared x
lgx minus two multiply by lg squared x
lgx-2*lg2x
lgx-2*lg²x
lgx-2*lg to the power of 2x
lgx-2lg^2x
lgx-2lg2x
Similar expressions
lgx+2*lg^2x

The derivative of the function/ lgx-2*lg^2x

Derivative of lgx-2*lg^2x

The solution

You have entered [src]

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

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

log(x) - 2*log(x)^2

Detail solution

Differentiate $- 2 \log{\left(x \right)}^{2} + \log{\left(x \right)}$ term by term:
1. The derivative of $\log{\left(x \right)}$ is $\frac{1}{x}$ .
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Let $u = \log{\left(x \right)}$ .
  2. Apply the power rule: $u^{2}$ goes to $2 u$
  3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \log{\left(x \right)}$ :
    1. The derivative of $\log{\left(x \right)}$ is $\frac{1}{x}$ .
    The result of the chain rule is:
    
    $\frac{2 \log{\left(x \right)}}{x}$
  So, the result is: $- \frac{4 \log{\left(x \right)}}{x}$
The result is: $- \frac{4 \log{\left(x \right)}}{x} + \frac{1}{x}$
Now simplify:

$\frac{1 - 4 \log{\left(x \right)}}{x}$

The answer is:

$\frac{1 - 4 \log{\left(x \right)}}{x}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

1   4*log(x)
- - --------
x      x

$$- \frac{4 \log{\left(x \right)}}{x} + \frac{1}{x}$$

Simplify

The second derivative [src]

-5 + 4*log(x)
-------------
       2     
      x

$$\frac{4 \log{\left(x \right)} - 5}{x^{2}}$$

Simplify

The third derivative [src]

2*(7 - 4*log(x))
----------------
        3       
       x

$$\frac{2 \left(7 - 4 \log{\left(x \right)}\right)}{x^{3}}$$

Simplify