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Derivative of:
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Identical expressions
y=√x^ three -2x
y equally √x cubed minus 2x
y equally √x to the power of three minus 2x
y=√x3-2x
y=√x³-2x
y=√x to the power of 3-2x
Similar expressions
y=√x^3+2x

The derivative of the function/ y=√x^3-2x

Derivative of y=√x^3-2x

The solution

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     3      
  ___       
\/ x   - 2*x

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

  /     3      \
d |  ___       |
--\\/ x   - 2*x/
dx

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

Transform

Detail solution

Differentiate $\left(\sqrt{x}\right)^{3} - 2 x$ 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. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Apply the power rule: $x$ goes to $1$
    So, the result is: $2$
  So, the result is: $-2$
The result is: $\frac{3 \sqrt{x}}{2} - 2$

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

        3/2
     3*x   
-2 + ------
      2*x

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

 -3   
------
   3/2
8*x

$$- \frac{3}{8 x^{\frac{3}{2}}}$$

Simplify

The graph

Derivative of y=√x^3-2x