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Derivative of:
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Integral of d{x}:
x^2*(x+3)
Identical expressions
x^ two *(x+ three)
x squared multiply by (x plus 3)
x to the power of two multiply by (x plus three)
x2*(x+3)
x2*x+3
x²*(x+3)
x to the power of 2*(x+3)
x^2(x+3)
x2(x+3)
x2x+3
x^2x+3
Similar expressions
x^2*(x-3)

The derivative of the function/ x^2*(x+3)

Derivative of x^2*(x+3)

The solution

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 2        
x *(x + 3)

$$x^{2} \left(x + 3\right)$$

x^2*(x + 3)

Detail solution

Apply the product rule:

$\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$

$f{\left(x \right)} = x^{2}$ ; to find $\frac{d}{d x} f{\left(x \right)}$ :
1. Apply the power rule: $x^{2}$ goes to $2 x$
$g{\left(x \right)} = x + 3$ ; to find $\frac{d}{d x} g{\left(x \right)}$ :
1. Differentiate $x + 3$ term by term:
  1. Apply the power rule: $x$ goes to $1$
  2. The derivative of the constant $3$ is zero.
  The result is: $1$
The result is: $x^{2} + 2 x \left(x + 3\right)$
Now simplify:

$3 x \left(x + 2\right)$

The answer is:

$3 x \left(x + 2\right)$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

 2              
x  + 2*x*(x + 3)

$$x^{2} + 2 x \left(x + 3\right)$$

Simplify

The second derivative [src]

6*(1 + x)

$$6 \left(x + 1\right)$$

Simplify

The third derivative [src]

$$6$$

Simplify

The graph

Derivative of x^2*(x+3)