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Identical expressions
y=(sqrt2x- five)(sqrt2x- five)
y equally ( square root of 2x minus 5)( square root of 2x minus 5)
y equally ( square root of 2x minus five)( square root of 2x minus five)
y=(√2x-5)(√2x-5)
y=sqrt2x-5sqrt2x-5
Similar expressions
y=(sqrt2x+5)(sqrt2x-5)
y=(sqrt2x-5)(sqrt2x+5)

The derivative of the function/ y=(sqrt2x-5)(sqrt2x-5)

Derivative of y=(sqrt2x-5)(sqrt2x-5)

The solution

You have entered [src]

/  _____    \ /  _____    \
\\/ 2*x  - 5/*\\/ 2*x  - 5/

$$\left(\sqrt{2 x} - 5\right) \left(\sqrt{2 x} - 5\right)$$

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

Detail solution

Apply the product rule:

$\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$

$f{\left(x \right)} = \sqrt{2 x} - 5$ ; to find $\frac{d}{d x} f{\left(x \right)}$ :
1. Differentiate $\sqrt{2 x} - 5$ term by term:
  1. Let $u = 2 x$ .
  2. Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$
  3. Then, apply the chain rule. Multiply by $\frac{d}{d x} 2 x$ :
    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: $2$
    The result of the chain rule is:
    
    $\frac{\sqrt{2}}{2 \sqrt{x}}$
  4. The derivative of the constant $-5$ is zero.
  The result is: $\frac{\sqrt{2}}{2 \sqrt{x}}$
$g{\left(x \right)} = \sqrt{2 x} - 5$ ; to find $\frac{d}{d x} g{\left(x \right)}$ :
1. Differentiate $\sqrt{2 x} - 5$ term by term:
  1. Let $u = 2 x$ .
  2. Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$
  3. Then, apply the chain rule. Multiply by $\frac{d}{d x} 2 x$ :
    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: $2$
    The result of the chain rule is:
    
    $\frac{\sqrt{2}}{2 \sqrt{x}}$
  4. The derivative of the constant $-5$ is zero.
  The result is: $\frac{\sqrt{2}}{2 \sqrt{x}}$
The result is: $\frac{\sqrt{2} \left(\sqrt{2 x} - 5\right)}{\sqrt{x}}$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

  ___ /  _____    \
\/ 2 *\\/ 2*x  - 5/
-------------------
         ___       
       \/ x

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

Simplify

The second derivative [src]

      ___ /       ___   ___\
1   \/ 2 *\-5 + \/ 2 *\/ x /
- - ------------------------
x               3/2         
             2*x

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

Simplify

The third derivative [src]

  /         ___ /       ___   ___\\
  |  2    \/ 2 *\-5 + \/ 2 *\/ x /|
3*|- -- + ------------------------|
  |   2              5/2          |
  \  x              x             /
-----------------------------------
                 4

$$\frac{3 \left(- \frac{2}{x^{2}} + \frac{\sqrt{2} \left(\sqrt{2} \sqrt{x} - 5\right)}{x^{\frac{5}{2}}}\right)}{4}$$

Simplify

The graph

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Derivative of y=(sqrt2x-5)(sqrt2x-5)

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The solution