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Derivative of:
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Integral of d{x}:
(2*x+1)^2
Identical expressions
(two *x+ one)^ two
(2 multiply by x plus 1) squared
(two multiply by x plus one) to the power of two
(2*x+1)2
2*x+12
(2*x+1)²
(2*x+1) to the power of 2
(2x+1)^2
(2x+1)2
2x+12
2x+1^2
Similar expressions
(2*x-1)^2

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

Derivative of (2*x+1)^2

The solution

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         2
(2*x + 1)

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

(2*x + 1)^2

Detail solution

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

$8 x + 4$

The answer is:

$8 x + 4$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

4 + 8*x

$$8 x + 4$$

Simplify

The second derivative [src]

$$8$$

Simplify

The third derivative [src]

$$0$$

Simplify

The graph

Derivative of (2*x+1)^2