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

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

Function f() - derivative -N order at the point
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The solution

You have entered [src] 
/  _____    \ /  _____    \
\\/ 2*x  - 5/*\\/ 2*x  - 5/
(2x−5)(2x−5)\left(\sqrt{2 x} - 5\right) \left(\sqrt{2 x} - 5\right) 
(sqrt(2*x) - 5)*(sqrt(2*x) - 5)
Detail solution

  1. Apply the product rule:

    ddxf(x)g(x)=f(x)ddxg(x)+g(x)ddxf(x)\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(x)=2x−5f{\left(x \right)} = \sqrt{2 x} - 5; to find ddxf(x)\frac{d}{d x} f{\left(x \right)}:

    1. Differentiate 2x−5\sqrt{2 x} - 5 term by term:

      1. Let u=2xu = 2 x.

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

      3. Then, apply the chain rule. Multiply by ddx2x\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: xx goes to 11

          So, the result is: 22

        The result of the chain rule is:

        22x\frac{\sqrt{2}}{2 \sqrt{x}}

      4. The derivative of the constant −5-5 is zero.

      The result is: 22x\frac{\sqrt{2}}{2 \sqrt{x}}

    g(x)=2x−5g{\left(x \right)} = \sqrt{2 x} - 5; to find ddxg(x)\frac{d}{d x} g{\left(x \right)}:

    1. Differentiate 2x−5\sqrt{2 x} - 5 term by term:

      1. Let u=2xu = 2 x.

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

      3. Then, apply the chain rule. Multiply by ddx2x\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: xx goes to 11

          So, the result is: 22

        The result of the chain rule is:

        22x\frac{\sqrt{2}}{2 \sqrt{x}}

      4. The derivative of the constant −5-5 is zero.

      The result is: 22x\frac{\sqrt{2}}{2 \sqrt{x}}

    The result is: 2(2x−5)x\frac{\sqrt{2} \left(\sqrt{2 x} - 5\right)}{\sqrt{x}}

  2. Now simplify:

    2−52x2 - \frac{5 \sqrt{2}}{\sqrt{x}}

The answer is:

2−52x2 - \frac{5 \sqrt{2}}{\sqrt{x}}

The graph
02468-8-6-4-2-1010-5050
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
  ___ /  _____    \
\/ 2 *\\/ 2*x  - 5/
-------------------
         ___       
       \/ x
2(2x−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
1x−2(2x−5)2x32\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
3(−2x2+2(2x−5)x52)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
Derivative of y=(sqrt2x-5)(sqrt2x-5)
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