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sqrt(3x-1)
The derivative of the function/ sqrt(3x-1)

Derivative of sqrt(3x-1)

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

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The solution

You have entered [src] 
  _________
\/ 3*x - 1
3x−1\sqrt{3 x - 1} 
d /  _________\
--\\/ 3*x - 1 /
dx
ddx3x−1\frac{d}{d x} \sqrt{3 x - 1}
Transform
Detail solution

  1. Let u=3x−1u = 3 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(3x−1)\frac{d}{d x} \left(3 x - 1\right):

    1. Differentiate 3x−13 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: 33

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

      The result is: 33

    The result of the chain rule is:

    323x−1\frac{3}{2 \sqrt{3 x - 1}}

  4. Now simplify:

    323x−1\frac{3}{2 \sqrt{3 x - 1}}

The answer is:

323x−1\frac{3}{2 \sqrt{3 x - 1}}

The graph
02468-8-6-4-2-1010010
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
      3      
-------------
    _________
2*\/ 3*x - 1
323x−1\frac{3}{2 \sqrt{3 x - 1}}
Simplify
The second derivative [src] 
      -9       
---------------
            3/2
4*(-1 + 3*x)
−94(3x−1)32- \frac{9}{4 \left(3 x - 1\right)^{\frac{3}{2}}}
Simplify
The third derivative [src] 
       81      
---------------
            5/2
8*(-1 + 3*x)
818(3x−1)52\frac{81}{8 \left(3 x - 1\right)^{\frac{5}{2}}}
Simplify
The graph
Derivative of sqrt(3x-1)
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