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Derivative of:
Derivative of (x^2+2x)^2
Derivative of sin(3*x)/(x+1)
Derivative of (pi*sin(pi*t/6))/2
Derivative of bx^2
Integral of d{x}:
(x^2+2x)^2
Identical expressions
(x^ two + two x)^2
(x squared plus 2x) squared
(x to the power of two plus two x) squared
(x2+2x)2
x2+2x2
(x²+2x)²
(x to the power of 2+2x) to the power of 2
x^2+2x^2
Similar expressions
(x^2-2x)^2

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

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

The solution

You have entered [src]

          2
/ 2      \ 
\x  + 2*x/

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

(x^2 + 2*x)^2

Detail solution

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

$\left(2 x + 2\right) \left(2 x^{2} + 4 x\right)$
Now simplify:

$4 x \left(x + 1\right) \left(x + 2\right)$

The answer is:

$4 x \left(x + 1\right) \left(x + 2\right)$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

          / 2      \
(4 + 4*x)*\x  + 2*x/

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

Simplify

The second derivative [src]

  / 2                  2\
4*\x  + 2*x + 2*(1 + x) /

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

Simplify

The third derivative [src]

24*(1 + x)

$$24 \left(x + 1\right)$$

Simplify

The graph

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