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sqrt(3*x-14)
The derivative of the function/ sqrt(3*x-14)

Derivative of sqrt(3*x-14)

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The solution

You have entered [src] 
  __________
\/ 3*x - 14
3x−14\sqrt{3 x - 14} 
sqrt(3*x - 14)
Detail solution

  1. Let u=3x−14u = 3 x - 14.

  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−14)\frac{d}{d x} \left(3 x - 14\right):

    1. Differentiate 3x−143 x - 14 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 −14-14 is zero.

      The result is: 33

    The result of the chain rule is:

    323x−14\frac{3}{2 \sqrt{3 x - 14}}

  4. Now simplify:

    323x−14\frac{3}{2 \sqrt{3 x - 14}}

The answer is:

323x−14\frac{3}{2 \sqrt{3 x - 14}}

The graph
02468-8-6-4-2-101005
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
      3       
--------------
    __________
2*\/ 3*x - 14
323x−14\frac{3}{2 \sqrt{3 x - 14}}
Simplify
The second derivative [src] 
      -9        
----------------
             3/2
4*(-14 + 3*x)
−94(3x−14)32- \frac{9}{4 \left(3 x - 14\right)^{\frac{3}{2}}}
Simplify
The third derivative [src] 
       81       
----------------
             5/2
8*(-14 + 3*x)
818(3x−14)52\frac{81}{8 \left(3 x - 14\right)^{\frac{5}{2}}}
Simplify
The graph
Derivative of sqrt(3*x-14)
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