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y=sqrt(4x+9)
The derivative of the function/ y=sqrt(4x+9)

Derivative of y=sqrt(4x+9)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  _________
\/ 4*x + 9
$$\sqrt{4 x + 9}$$ 
d /  _________\
--\\/ 4*x + 9 /
dx
$$\frac{d}{d x} \sqrt{4 x + 9}$$
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 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] 
     2     
-----------
  _________
\/ 4*x + 9
$$\frac{2}{\sqrt{4 x + 9}}$$
Simplify
The second derivative [src] 
    -4      
------------
         3/2
(9 + 4*x)
$$- \frac{4}{\left(4 x + 9\right)^{\frac{3}{2}}}$$
Simplify
The third derivative [src] 
     24     
------------
         5/2
(9 + 4*x)
$$\frac{24}{\left(4 x + 9\right)^{\frac{5}{2}}}$$
Simplify
The graph
Derivative of y=sqrt(4x+9)
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