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Derivative of:
Derivative of cos(5-3*x)
Derivative of cos^3(t)
Derivative of asin(y^2)
Derivative of (5x^2+2)×(x^2-4)^3
Integral of d{x}:
1/4(x+1)^2
Identical expressions
one / four (x+ one)^ two
1 divide by 4(x plus 1) squared
one divide by four (x plus one) to the power of two
1/4(x+1)2
1/4x+12
1/4(x+1)²
1/4(x+1) to the power of 2
1/4x+1^2
1 divide by 4(x+1)^2
Similar expressions
1/4(x-1)^2

The derivative of the function/ 1/4(x+1)^2

Derivative of 1/4(x+1)^2

The solution

You have entered [src]

       2
(x + 1) 
--------
   4

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

(x + 1)^2/4

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = x + 1$ .
2. Apply the power rule: $u^{2}$ goes to $2 u$
3. 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:
  
  $2 x + 2$
So, the result is: $\frac{x}{2} + \frac{1}{2}$

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

1   x
- + -
2   2

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

Simplify

The second derivative [src]

1/2

$$\frac{1}{2}$$

Simplify

The third derivative [src]

$$0$$

Simplify

The graph

Derivative of 1/4(x+1)^2