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Derivative of:
Derivative of e^x*x^2
Derivative of 2*sqrt(x^3)
Derivative of (x-4)^3
Derivative of x^3-5x
Graphing y =:
2*sqrt(x^3)
Identical expressions
two *sqrt(x^ three)
2 multiply by square root of (x cubed )
two multiply by square root of (x to the power of three)
2*√(x^3)
2*sqrt(x3)
2*sqrtx3
2*sqrt(x³)
2*sqrt(x to the power of 3)
2sqrt(x^3)
2sqrt(x3)
2sqrtx3
2sqrtx^3

The derivative of the function/ 2*sqrt(x^3)

Derivative of 2*sqrt(x^3)

The solution

You have entered [src]

     ____
    /  3 
2*\/  x

$$2 \sqrt{x^{3}}$$

2*sqrt(x^3)

Detail solution

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

The answer is:

$\frac{3 x^{2}}{\sqrt{x^{3}}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

     ____
    /  3 
3*\/  x  
---------
    x

$$\frac{3 \sqrt{x^{3}}}{x}$$

Simplify

The second derivative [src]

     ____
    /  3 
3*\/  x  
---------
      2  
   2*x

$$\frac{3 \sqrt{x^{3}}}{2 x^{2}}$$

Simplify

The third derivative [src]

      ____
     /  3 
-3*\/  x  
----------
      3   
   4*x

$$- \frac{3 \sqrt{x^{3}}}{4 x^{3}}$$

Simplify

The graph

Derivative of 2*sqrt(x^3)