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sqrt(3x+2)
The derivative of the function/ sqrt(3x+2)

Derivative of sqrt(3x+2)

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

You have entered [src] 
  _________
\/ 3*x + 2
3x+2\sqrt{3 x + 2} 
d /  _________\
--\\/ 3*x + 2 /
dx
ddx3x+2\frac{d}{d x} \sqrt{3 x + 2}
Transform
Detail solution

  1. Let u=3x+2u = 3 x + 2.

  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+2)\frac{d}{d x} \left(3 x + 2\right):

    1. Differentiate 3x+23 x + 2 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 22 is zero.

      The result is: 33

    The result of the chain rule is:

    323x+2\frac{3}{2 \sqrt{3 x + 2}}

  4. Now simplify:

    323x+2\frac{3}{2 \sqrt{3 x + 2}}

The answer is:

323x+2\frac{3}{2 \sqrt{3 x + 2}}

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 + 2
323x+2\frac{3}{2 \sqrt{3 x + 2}}
Simplify
The second derivative [src] 
     -9       
--------------
           3/2
4*(2 + 3*x)
−94(3x+2)32- \frac{9}{4 \left(3 x + 2\right)^{\frac{3}{2}}}
Simplify
The third derivative [src] 
      81      
--------------
           5/2
8*(2 + 3*x)
818(3x+2)52\frac{81}{8 \left(3 x + 2\right)^{\frac{5}{2}}}
Simplify
The graph
Derivative of sqrt(3x+2)
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