Mister Exam

Other calculators

y=sqrt(3x+1)
The derivative of the function/ y=sqrt(3x+1)

Derivative of y=sqrt(3x+1)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  _________
\/ 3*x + 1
$$\sqrt{3 x + 1}$$ 
d /  _________\
--\\/ 3*x + 1 /
dx
$$\frac{d}{d x} \sqrt{3 x + 1}$$
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] 
      3      
-------------
    _________
2*\/ 3*x + 1
$$\frac{3}{2 \sqrt{3 x + 1}}$$
Simplify
The second derivative [src] 
     -9       
--------------
           3/2
4*(1 + 3*x)
$$- \frac{9}{4 \left(3 x + 1\right)^{\frac{3}{2}}}$$
Simplify
The third derivative [src] 
      81      
--------------
           5/2
8*(1 + 3*x)
$$\frac{81}{8 \left(3 x + 1\right)^{\frac{5}{2}}}$$
Simplify
The graph
Derivative of y=sqrt(3x+1)
    © Mister Exam – Calculator