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sqrt(5x-1)
The derivative of the function/ sqrt(5x-1)

Derivative of sqrt(5x-1)

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

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The solution

You have entered [src] 
  _________
\/ 5*x - 1
5x−1\sqrt{5 x - 1} 
d /  _________\
--\\/ 5*x - 1 /
dx
ddx5x−1\frac{d}{d x} \sqrt{5 x - 1}
Transform
Detail solution

  1. Let u=5x−1u = 5 x - 1.

  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(5x−1)\frac{d}{d x} \left(5 x - 1\right):

    1. Differentiate 5x−15 x - 1 term by term:

      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: 55

      2. The derivative of the constant (−1)1\left(-1\right) 1 is zero.

      The result is: 55

    The result of the chain rule is:

    525x−1\frac{5}{2 \sqrt{5 x - 1}}

  4. Now simplify:

    525x−1\frac{5}{2 \sqrt{5 x - 1}}

The answer is:

525x−1\frac{5}{2 \sqrt{5 x - 1}}

The graph
02468-8-6-4-2-1010010
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
      5      
-------------
    _________
2*\/ 5*x - 1
525x−1\frac{5}{2 \sqrt{5 x - 1}}
Simplify
The second derivative [src] 
      -25      
---------------
            3/2
4*(-1 + 5*x)
−254(5x−1)32- \frac{25}{4 \left(5 x - 1\right)^{\frac{3}{2}}}
Simplify
The third derivative [src] 
      375      
---------------
            5/2
8*(-1 + 5*x)
3758(5x−1)52\frac{375}{8 \left(5 x - 1\right)^{\frac{5}{2}}}
Simplify
The graph
Derivative of sqrt(5x-1)
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