Mister Exam

Derivative of -sqrt(3x+4)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   _________
-\/ 3*x + 4 
$$- \sqrt{3 x + 4}$$
-sqrt(3*x + 4)
Detail solution
  1. The derivative of a constant times a function is the constant times the derivative of the function.

    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:

    So, the result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
     -3      
-------------
    _________
2*\/ 3*x + 4 
$$- \frac{3}{2 \sqrt{3 x + 4}}$$
The second derivative [src]
      9       
--------------
           3/2
4*(4 + 3*x)   
$$\frac{9}{4 \left(3 x + 4\right)^{\frac{3}{2}}}$$
The third derivative [src]
     -81      
--------------
           5/2
8*(4 + 3*x)   
$$- \frac{81}{8 \left(3 x + 4\right)^{\frac{5}{2}}}$$