Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of x^x
Derivative of ln(sin(x))
Derivative of tg6x
Derivative of ctg5x
Identical expressions
y=log5(x)-√xx^ six
y equally logarithm of 5(x) minus √xx to the power of 6
y equally logarithm of 5(x) minus √xx to the power of six
y=log5(x)-√xx6
y=log5x-√xx6
y=log5(x)-√xx⁶
y=log5x-√xx^6
Similar expressions
y=log5(x)+√xx^6

The derivative of the function/ y=log5(x)-√xx^6

Derivative of y=log5(x)-√xx^6

The solution

You have entered [src]

                6
log(x)     _____ 
------ - \/ x*x  
log(5)

$$- \left(\sqrt{x x}\right)^{6} + \frac{\log{\left(x \right)}}{\log{\left(5 \right)}}$$

  /                6\
d |log(x)     _____ |
--|------ - \/ x*x  |
dx\log(5)           /

$$\frac{d}{d x} \left(- \left(\sqrt{x x}\right)^{6} + \frac{\log{\left(x \right)}}{\log{\left(5 \right)}}\right)$$

Transform

Detail solution

Differentiate $- \left(\sqrt{x x}\right)^{6} + \frac{\log{\left(x \right)}}{\log{\left(5 \right)}}$ 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: $\frac{1}{x \log{\left(5 \right)}}$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Let $u = \sqrt{x x}$ .
  2. Apply the power rule: $u^{6}$ goes to $6 u^{5}$
  3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \sqrt{x x}$ :
    1. Let $u = x x$ .
    2. Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$
    3. Then, apply the chain rule. Multiply by $\frac{d}{d x} x x$ :
      1. Apply the product rule:
        
        $\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$
        
        $f{\left(x \right)} = x$ ; to find $\frac{d}{d x} f{\left(x \right)}$ :
        
        Apply the power rule: $x$ goes to $1$
        
        $g{\left(x \right)} = x$ ; to find $\frac{d}{d x} g{\left(x \right)}$ :
        
        Apply the power rule: $x$ goes to $1$
        
        The result is: $2 x$
      The result of the chain rule is:
      
      $\frac{x}{\left|{x}\right|}$
    The result of the chain rule is:
    
    $6 x^{5}$
  So, the result is: $- 6 x^{5}$
The result is: $- 6 x^{5} + \frac{1}{x \log{\left(5 \right)}}$

The answer is:

$- 6 x^{5} + \frac{1}{x \log{\left(5 \right)}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

     5      1    
- 6*x  + --------
         x*log(5)

$$- 6 x^{5} + \frac{1}{x \log{\left(5 \right)}}$$

Simplify

The second derivative [src]

 /    4       1    \
-|30*x  + ---------|
 |         2       |
 \        x *log(5)/

$$- (30 x^{4} + \frac{1}{x^{2} \log{\left(5 \right)}})$$

Simplify

The third derivative [src]

  /      3       1    \
2*|- 60*x  + ---------|
  |           3       |
  \          x *log(5)/

$$2 \left(- 60 x^{3} + \frac{1}{x^{3} \log{\left(5 \right)}}\right)$$

Simplify

The graph

Other calculators

How to use it?

Identical expressions

Similar expressions

Derivative of y=log5(x)-√xx^6

The graph:

Piecewise:

The solution