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Derivative of:
Derivative of sin(x/3)^(2)*cot(x/2)
Derivative of atan(sqrt(x))
Derivative of atan(2*x)
Derivative of cos(2*x-3)
Integral of d{x}:
(x+1)^(1/2)
Graphing y =:
(x+1)^(1/2)
Identical expressions
(x+ one)^(one / two)
(x plus 1) to the power of (1 divide by 2)
(x plus one) to the power of (one divide by two)
(x+1)(1/2)
x+11/2
x+1^1/2
(x+1)^(1 divide by 2)
Similar expressions
(2cosx+1)^(1/2)
(x-1)^(1/2)

The derivative of the function/ (x+1)^(1/2)

Derivative of (x+1)^(1/2)

The solution

You have entered [src]

  _______
\/ x + 1

$$\sqrt{x + 1}$$

sqrt(x + 1)

Detail solution

Let $u = x + 1$ .
Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x + 1\right)$ :
1. Differentiate $x + 1$ term by term:
  1. Apply the power rule: $x$ goes to $1$
  2. The derivative of the constant $1$ is zero.
  The result is: $1$
The result of the chain rule is:

$\frac{1}{2 \sqrt{x + 1}}$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

     1     
-----------
    _______
2*\/ x + 1

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

Simplify

The second derivative [src]

    -1      
------------
         3/2
4*(1 + x)

$$- \frac{1}{4 \left(x + 1\right)^{\frac{3}{2}}}$$

Simplify

The third derivative [src]

     3      
------------
         5/2
8*(1 + x)

$$\frac{3}{8 \left(x + 1\right)^{\frac{5}{2}}}$$

Simplify

The graph

Derivative of (x+1)^(1/2)