Mister Exam

Other calculators

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

Derivative of sqrt(x+1)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  _______
\/ x + 1
x+1\sqrt{x + 1} 
sqrt(x + 1)
Detail solution

  1. Let u=x+1u = x + 1.

  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(x+1)\frac{d}{d x} \left(x + 1\right):

    1. Differentiate x+1x + 1 term by term:

      1. Apply the power rule: xx goes to 11

      2. The derivative of the constant 11 is zero.

      The result is: 11

    The result of the chain rule is:

    12x+1\frac{1}{2 \sqrt{x + 1}}

  4. Now simplify:

    12x+1\frac{1}{2 \sqrt{x + 1}}

The answer is:

12x+1\frac{1}{2 \sqrt{x + 1}}

The graph
02468-8-6-4-2-101005
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
     1     
-----------
    _______
2*\/ x + 1
12x+1\frac{1}{2 \sqrt{x + 1}}
Simplify
The second derivative [src] 
    -1      
------------
         3/2
4*(1 + x)
−14(x+1)32- \frac{1}{4 \left(x + 1\right)^{\frac{3}{2}}}
Simplify
The third derivative [src] 
     3      
------------
         5/2
8*(1 + x)
38(x+1)52\frac{3}{8 \left(x + 1\right)^{\frac{5}{2}}}
Simplify
The graph
Derivative of sqrt(x+1)
    © Mister Exam – Calculator