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x-2*sqrt(5-x^2)

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Derivative of:
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Identical expressions
x- two *sqrt(five -x^ two)
x minus 2 multiply by square root of (5 minus x squared )
x minus two multiply by square root of (five minus x to the power of two)
x-2*√(5-x^2)
x-2*sqrt(5-x2)
x-2*sqrt5-x2
x-2*sqrt(5-x²)
x-2*sqrt(5-x to the power of 2)
x-2sqrt(5-x^2)
x-2sqrt(5-x2)
x-2sqrt5-x2
x-2sqrt5-x^2
Similar expressions
x-2*sqrt(5+x^2)
x+2*sqrt(5-x^2)

The derivative of the function/ x-2*sqrt(5-x^2)

Derivative of x-2*sqrt(5-x^2)

The solution

You have entered [src]

         ________
        /      2 
x - 2*\/  5 - x

$$x - 2 \sqrt{5 - x^{2}}$$

Transform

Detail solution

Differentiate $x - 2 \sqrt{5 - x^{2}}$ term by term:
1. Apply the power rule: $x$ goes to $1$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Let $u = 5 - x^{2}$ .
  2. Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$
  3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(5 - x^{2}\right)$ :
    1. Differentiate $5 - x^{2}$ term by term:
      1. The derivative of the constant $5$ is zero.
      2. The derivative of a constant times a function is the constant times the derivative of the function.
        
        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:
    
    $- \frac{x}{\sqrt{5 - x^{2}}}$
  So, the result is: $\frac{2 x}{\sqrt{5 - x^{2}}}$
The result is: $\frac{2 x}{\sqrt{5 - x^{2}}} + 1$

The answer is:

$\frac{2 x}{\sqrt{5 - x^{2}}} + 1$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

        2*x    
1 + -----------
       ________
      /      2 
    \/  5 - x

$$\frac{2 x}{\sqrt{5 - x^{2}}} + 1$$

Simplify

The second derivative [src]

  /       2  \
  |      x   |
2*|1 + ------|
  |         2|
  \    5 - x /
--------------
    ________  
   /      2   
 \/  5 - x

$$\frac{2 \left(\frac{x^{2}}{5 - x^{2}} + 1\right)}{\sqrt{5 - x^{2}}}$$

Simplify

The third derivative [src]

    /       2  \
    |      x   |
6*x*|1 + ------|
    |         2|
    \    5 - x /
----------------
          3/2   
  /     2\      
  \5 - x /

$$\frac{6 x \left(\frac{x^{2}}{5 - x^{2}} + 1\right)}{\left(5 - x^{2}\right)^{\frac{3}{2}}}$$

Simplify

The graph

Derivative of x-2*sqrt(5-x^2)