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

Derivative of sqrt(2-3x^2)

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   __________
  /        2 
\/  2 - 3*x
−3x2+2\sqrt{- 3 x^{2} + 2} 
  /   __________\
d |  /        2 |
--\\/  2 - 3*x  /
dx
ddx−3x2+2\frac{d}{d x} \sqrt{- 3 x^{2} + 2}
Transform
Detail solution

  1. Let u=2−3x2u = 2 - 3 x^{2}.

  2. Apply the power rule: u\sqrt{u} goes to 12u\frac{1}{2 \sqrt{u}}

  3. Then, apply the chain rule. Multiply by ddx(2−3x2)\frac{d}{d x} \left(2 - 3 x^{2}\right):

    1. Differentiate 2−3x22 - 3 x^{2} term by term:

      1. The derivative of the constant 22 is zero.

      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.

          1. Apply the power rule: x2x^{2} goes to 2x2 x

          So, the result is: 6x6 x

        So, the result is: −6x- 6 x

      The result is: −6x- 6 x

    The result of the chain rule is:

    −3x2−3x2- \frac{3 x}{\sqrt{2 - 3 x^{2}}}

  4. Now simplify:

    −3x2−3x2- \frac{3 x}{\sqrt{2 - 3 x^{2}}}

The answer is:

−3x2−3x2- \frac{3 x}{\sqrt{2 - 3 x^{2}}}

The graph
02468-8-6-4-2-10105-5
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
     -3*x    
-------------
   __________
  /        2 
\/  2 - 3*x
−3x−3x2+2- \frac{3 x}{\sqrt{- 3 x^{2} + 2}}
Simplify
The second derivative [src] 
   /         2  \
   |      3*x   |
-3*|1 + --------|
   |           2|
   \    2 - 3*x /
-----------------
     __________  
    /        2   
  \/  2 - 3*x
−3⋅(3x2−3x2+2+1)−3x2+2- \frac{3 \cdot \left(\frac{3 x^{2}}{- 3 x^{2} + 2} + 1\right)}{\sqrt{- 3 x^{2} + 2}}
Simplify
The third derivative [src] 
      /         2  \
      |      3*x   |
-27*x*|1 + --------|
      |           2|
      \    2 - 3*x /
--------------------
             3/2    
   /       2\       
   \2 - 3*x /
−27x(3x2−3x2+2+1)(−3x2+2)32- \frac{27 x \left(\frac{3 x^{2}}{- 3 x^{2} + 2} + 1\right)}{\left(- 3 x^{2} + 2\right)^{\frac{3}{2}}}
Simplify
The graph
Derivative of sqrt(2-3x^2)
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