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Derivative of:
Derivative of 2x²
Derivative of sin(x)*cos(x)+x
Derivative of sin^2*2x
Derivative of ln(x+3)
Identical expressions
sqrtx^ three -sqrtx+ two
square root of x cubed minus square root of x plus 2
square root of x to the power of three minus square root of x plus two
√x^3-√x+2
sqrtx3-sqrtx+2
sqrtx³-sqrtx+2
sqrtx to the power of 3-sqrtx+2
Similar expressions
sqrtx^3-sqrtx-2
sqrtx^3+sqrtx+2

The derivative of the function/ sqrtx^3-sqrtx+2

Derivative of sqrtx^3-sqrtx+2

The solution

You have entered [src]

     3            
  ___      ___    
\/ x   - \/ x  + 2

$$\left(\left(\sqrt{x}\right)^{3} - \sqrt{x}\right) + 2$$

(sqrt(x))^3 - sqrt(x) + 2

Detail solution

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

$\frac{3 x - 1}{2 \sqrt{x}}$

The answer is:

$\frac{3 x - 1}{2 \sqrt{x}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

               3/2
     1      3*x   
- ------- + ------
      ___    2*x  
  2*\/ x

$$\frac{3 x^{\frac{3}{2}}}{2 x} - \frac{1}{2 \sqrt{x}}$$

Simplify

The second derivative [src]

     1 
 3 + - 
     x 
-------
    ___
4*\/ x

$$\frac{3 + \frac{1}{x}}{4 \sqrt{x}}$$

Simplify

The third derivative [src]

   /    1\
-3*|1 + -|
   \    x/
----------
     3/2  
  8*x

$$- \frac{3 \left(1 + \frac{1}{x}\right)}{8 x^{\frac{3}{2}}}$$

Simplify