Derivative of 3(sqrt(4-x²))

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     ________
    /      2 
3*\/  4 - x

$$3 \sqrt{4 - x^{2}}$$

3*sqrt(4 - x^2)

Detail solution

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

The answer is:

$- \frac{3 x}{\sqrt{4 - x^{2}}}$

The graph

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The first derivative [src]

    -3*x   
-----------
   ________
  /      2 
\/  4 - x

$$- \frac{3 x}{\sqrt{4 - x^{2}}}$$

Simplify

The second derivative [src]

  /         2  \
  |        x   |
3*|-1 + -------|
  |           2|
  \     -4 + x /
----------------
     ________   
    /      2    
  \/  4 - x

$$\frac{3 \left(\frac{x^{2}}{x^{2} - 4} - 1\right)}{\sqrt{4 - x^{2}}}$$

Simplify

The third derivative [src]

    /         2  \
    |        x   |
9*x*|-1 + -------|
    |           2|
    \     -4 + x /
------------------
           3/2    
   /     2\       
   \4 - x /

$$\frac{9 x \left(\frac{x^{2}}{x^{2} - 4} - 1\right)}{\left(4 - x^{2}\right)^{\frac{3}{2}}}$$

Simplify

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Derivative of 3(sqrt(4-x²))

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