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Derivative of:
Derivative of 3^(2*x)
Derivative of (x-3)^4
Derivative of ln(1+x)
Derivative of ln(1-x)
Identical expressions
- six x^ eight -4sqrtx^ five / nine - seven /x^6+3sqrt3^ one / eight
minus 6x to the power of 8 minus 4 square root of x to the power of 5 divide by 9 minus 7 divide by x to the power of 6 plus 3 square root of 3 to the power of 1 divide by 8
minus six x to the power of eight minus 4 square root of x to the power of five divide by nine minus seven divide by x to the power of 6 plus 3 square root of 3 to the power of one divide by eight
-6x^8-4√x^5/9-7/x^6+3√3^1/8
-6x8-4sqrtx5/9-7/x6+3sqrt31/8
-6x⁸-4sqrtx⁵/9-7/x⁶+3sqrt3^1/8
-6x^8-4sqrtx^5 divide by 9-7 divide by x^6+3sqrt3^1 divide by 8
Similar expressions
-6x^8-4sqrtx^5/9+7/x^6+3sqrt3^1/8
6x^8-4sqrtx^5/9-7/x^6+3sqrt3^1/8
-6x^8-4sqrtx^5/9-7/x^6-3sqrt3^1/8
-6x^8+4sqrtx^5/9-7/x^6+3sqrt3^1/8
What you mean?
x^8*(-6) - 4*(sqrt(x))^5/9 - 7/x^6 + 3*(sqrt(3))^(1/8)
x^8*(-6) - 4*(sqrt(x))^(5/9) - 7/x^6 + 3*(sqrt(3))^(1/8)
x^8*(-6) - 4*(sqrt(x))^(5/9 - 7)/x^6 + 3*(sqrt(3))^(1/8)
x^8*(-6) - 4*(sqrt(x))^(5/(9 - 7))/x^6 + 3*(sqrt(3))^(1/8)
x^8*(-6) - 4*(sqrt(x))^(5/(9 - 7))/x^6 + 3*(sqrt(3))^(1/8)

The derivative of the function/ -6x^8-4sqrtx^5/9-7/x^6+3sqrt3^1/8

You entered:

-6x^8-4sqrtx^5/9-7/x^6+3sqrt3^1/8

What you mean?

x^8*(-6) - 4*(sqrt(x))^5/9 - 7/x^6 + 3*(sqrt(3))^(1/8)

x^8*(-6) - 4*(sqrt(x))^(5/9) - 7/x^6 + 3*(sqrt(3))^(1/8)

x^8*(-6) - 4*(sqrt(x))^(5/9 - 7)/x^6 + 3*(sqrt(3))^(1/8)

x^8*(-6) - 4*(sqrt(x))^(5/(9 - 7))/x^6 + 3*(sqrt(3))^(1/8)

x^8*(-6) - 4*(sqrt(x))^(5/(9 - 7))/x^6 + 3*(sqrt(3))^(1/8)

Derivative of -6x^8-4sqrtx^5/9-7/x^6+3sqrt3^1/8

The solution

You have entered [src]

                5                    
             ___              _______
     8   4*\/ x     7      8 /   ___ 
- 6*x  - -------- - -- + 3*\/  \/ 3  
            9        6               
                    x

$$\left(\left(- 6 x^{8} - \frac{4 \left(\sqrt{x}\right)^{5}}{9}\right) - \frac{7}{x^{6}}\right) + 3 \sqrt[8]{\sqrt{3}}$$

Transform

Detail solution

Differentiate $\left(\left(- 6 x^{8} - \frac{4 \left(\sqrt{x}\right)^{5}}{9}\right) - \frac{7}{x^{6}}\right) + 3 \sqrt[8]{\sqrt{3}}$ term by term:
1. Differentiate $\left(- 6 x^{8} - \frac{4 \left(\sqrt{x}\right)^{5}}{9}\right) - \frac{7}{x^{6}}$ term by term:
  1. Differentiate $- 6 x^{8} - \frac{4 \left(\sqrt{x}\right)^{5}}{9}$ term by term:
    1. The derivative of a constant times a function is the constant times the derivative of the function.
      1. Apply the power rule: $x^{8}$ goes to $8 x^{7}$
      So, the result is: $- 48 x^{7}$
    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.
        
        Let $u = \sqrt{x}$ .
        
        Apply the power rule: $u^{5}$ goes to $5 u^{4}$
        
        Then, apply the chain rule. Multiply by $\frac{d}{d x} \sqrt{x}$ :
        
        Apply the power rule: $\sqrt{x}$ goes to $\frac{1}{2 \sqrt{x}}$
        
        The result of the chain rule is:
        
        $\frac{5 x^{\frac{3}{2}}}{2}$
        
        So, the result is: $10 x^{\frac{3}{2}}$
      So, the result is: $- \frac{10 x^{\frac{3}{2}}}{9}$
    The result is: $- \frac{10 x^{\frac{3}{2}}}{9} - 48 x^{7}$
  2. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Let $u = x^{6}$ .
    2. Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$
    3. Then, apply the chain rule. Multiply by $\frac{d}{d x} x^{6}$ :
      1. Apply the power rule: $x^{6}$ goes to $6 x^{5}$
      The result of the chain rule is:
      
      $- \frac{6}{x^{7}}$
    So, the result is: $\frac{42}{x^{7}}$
  The result is: $- \frac{10 x^{\frac{3}{2}}}{9} - 48 x^{7} + \frac{42}{x^{7}}$
2. The derivative of the constant $3 \sqrt[8]{\sqrt{3}}$ is zero.
The result is: $- \frac{10 x^{\frac{3}{2}}}{9} - 48 x^{7} + \frac{42}{x^{7}}$
Now simplify:

$\frac{- \frac{10 x^{\frac{17}{2}}}{9} - 48 x^{14} + 42}{x^{7}}$

The answer is:

$\frac{- \frac{10 x^{\frac{17}{2}}}{9} - 48 x^{14} + 42}{x^{7}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

                   3/2
      7   42   10*x   
- 48*x  + -- - -------
           7      9   
          x

$$- \frac{10 x^{\frac{3}{2}}}{9} - 48 x^{7} + \frac{42}{x^{7}}$$

Simplify

The second derivative [src]

 /                   ___\
 |294        6   5*\/ x |
-|--- + 336*x  + -------|
 |  8               3   |
 \ x                    /

$$- (\frac{5 \sqrt{x}}{3} + 336 x^{6} + \frac{294}{x^{8}})$$

Simplify

The third derivative [src]

        5   2352      5   
- 2016*x  + ---- - -------
              9        ___
             x     6*\/ x

$$- 2016 x^{5} + \frac{2352}{x^{9}} - \frac{5}{6 \sqrt{x}}$$

Simplify

The graph

Derivative of -6x^8-4sqrtx^5/9-7/x^6+3sqrt3^1/8

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Identical expressions

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What you mean?

Derivative of -6x^8-4sqrtx^5/9-7/x^6+3sqrt3^1/8

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The solution