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sqrt(14x^2+16x+23)
The derivative of the function/ sqrt(14x^2+16x+23)

Derivative of sqrt(14x^2+16x+23)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   ___________________
  /     2             
\/  14*x  + 16*x + 23
$$\sqrt{14 x^{2} + 16 x + 23}$$ 
  /   ___________________\
d |  /     2             |
--\\/  14*x  + 16*x + 23 /
dx
$$\frac{d}{d x} \sqrt{14 x^{2} + 16 x + 23}$$
Transform
Detail solution

  1. Let .

  2. Apply the power rule: goes to

  3. Then, apply the chain rule. Multiply by :

    1. Differentiate 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: goes to

        So, the result is:

      2. The derivative of a constant times a function is the constant times the derivative of the function.

        1. Apply the power rule: goes to

        So, the result is:

      3. The derivative of the constant is zero.

      The result is:

    The result of the chain rule is:

  4. Now simplify:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
       8 + 14*x       
----------------------
   ___________________
  /     2             
\/  14*x  + 16*x + 23
$$\frac{14 x + 8}{\sqrt{14 x^{2} + 16 x + 23}}$$
Simplify
The second derivative [src] 
  /                  2  \
  |       2*(4 + 7*x)   |
2*|7 - -----------------|
  |             2       |
  \    23 + 14*x  + 16*x/
-------------------------
     ___________________ 
    /          2         
  \/  23 + 14*x  + 16*x
$$\frac{2 \left(- \frac{2 \left(7 x + 4\right)^{2}}{14 x^{2} + 16 x + 23} + 7\right)}{\sqrt{14 x^{2} + 16 x + 23}}$$
Simplify
The third derivative [src] 
   /                   2  \          
   |        2*(4 + 7*x)   |          
12*|-7 + -----------------|*(4 + 7*x)
   |              2       |          
   \     23 + 14*x  + 16*x/          
-------------------------------------
                           3/2       
        /         2       \          
        \23 + 14*x  + 16*x/
$$\frac{12 \cdot \left(7 x + 4\right) \left(\frac{2 \left(7 x + 4\right)^{2}}{14 x^{2} + 16 x + 23} - 7\right)}{\left(14 x^{2} + 16 x + 23\right)^{\frac{3}{2}}}$$
Simplify
The graph
Derivative of sqrt(14x^2+16x+23)
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