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y=sqrt(3x+4)
The derivative of the function/ y=sqrt(3x+4)

Derivative of y=sqrt(3x+4)

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

You have entered [src] 
  _________
\/ 3*x + 4
3x+4\sqrt{3 x + 4} 
d /  _________\
--\\/ 3*x + 4 /
dx
ddx3x+4\frac{d}{d x} \sqrt{3 x + 4}
Transform
Detail solution

  1. Let u=3x+4u = 3 x + 4.

  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+4)\frac{d}{d x} \left(3 x + 4\right):

    1. Differentiate 3x+43 x + 4 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 44 is zero.

      The result is: 33

    The result of the chain rule is:

    323x+4\frac{3}{2 \sqrt{3 x + 4}}

  4. Now simplify:

    323x+4\frac{3}{2 \sqrt{3 x + 4}}

The answer is:

323x+4\frac{3}{2 \sqrt{3 x + 4}}

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