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Derivative of:
Derivative of e^x-7
Derivative of 3*x^5-2*x^2
Derivative of sqrt(x)-1/(sqrt(x)*2-x-1)
Derivative of 3*x^2-4*x+2
Identical expressions
two (sqrtx^ one / three)
2( square root of x to the power of 1 divide by 3)
two ( square root of x to the power of one divide by three)
2(√x^1/3)
2(sqrtx1/3)
2sqrtx1/3
2sqrtx^1/3
2(sqrtx^1 divide by 3)

The derivative of the function/ 2(sqrtx^1/3)

Derivative of 2(sqrtx^1/3)

The solution

You have entered [src]

     _______
  3 /   ___ 
2*\/  \/ x

$$2 \sqrt[3]{\sqrt{x}}$$

2*(sqrt(x))^(1/3)

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = \sqrt{x}$ .
2. Apply the power rule: $\sqrt[3]{u}$ goes to $\frac{1}{3 u^{\frac{2}{3}}}$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \sqrt{x}$ :
  1. Apply the power rule: $\sqrt{x}$ goes to $\frac{1}{2 \sqrt{x}}$
  The result of the chain rule is:
  
  $\frac{1}{6 x^{\frac{5}{6}}}$
So, the result is: $\frac{1}{3 x^{\frac{5}{6}}}$

The answer is:

$\frac{1}{3 x^{\frac{5}{6}}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

  1   
------
   5/6
3*x

$$\frac{1}{3 x^{\frac{5}{6}}}$$

Simplify

The second derivative [src]

  -5    
--------
    11/6
18*x

$$- \frac{5}{18 x^{\frac{11}{6}}}$$

Simplify

The third derivative [src]

    55   
---------
     17/6
108*x

$$\frac{55}{108 x^{\frac{17}{6}}}$$

Simplify