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Derivative of:
Derivative of 1/3*x^3
Derivative of x^2/(x^2+1)
Derivative of x^(5/2)
Derivative of (x+3)^2*(x+5)-1
Identical expressions
x^ two *(x+ four)
x squared multiply by (x plus 4)
x to the power of two multiply by (x plus four)
x2*(x+4)
x2*x+4
x²*(x+4)
x to the power of 2*(x+4)
x^2(x+4)
x2(x+4)
x2x+4
x^2x+4
Similar expressions
x^2*(x-4)

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

Derivative of x^2*(x+4)

The solution

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 2        
x *(x + 4)

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

x^2*(x + 4)

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 $2 x$
$g{\left(x \right)} = x + 4$ ; to find $\frac{d}{d x} g{\left(x \right)}$ :
1. Differentiate $x + 4$ term by term:
  1. Apply the power rule: $x$ goes to $1$
  2. The derivative of the constant $4$ is zero.
  The result is: $1$
The result is: $x^{2} + 2 x \left(x + 4\right)$
Now simplify:

$x \left(3 x + 8\right)$

The answer is:

$x \left(3 x + 8\right)$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

 2              
x  + 2*x*(x + 4)

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

Simplify

The second derivative [src]

2*(4 + 3*x)

$$2 \left(3 x + 4\right)$$

Simplify

The third derivative [src]

$$6$$

Simplify