Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of x^3/cosx
Derivative of (4-3*x)^7
Derivative of 3x²-2
Derivative of 2^x*sin(x)
Graphing y =:
x^2*(x+3)-2
Identical expressions
x^ two *(x+ three)- two
x squared multiply by (x plus 3) minus 2
x to the power of two multiply by (x plus three) minus two
x2*(x+3)-2
x2*x+3-2
x²*(x+3)-2
x to the power of 2*(x+3)-2
x^2(x+3)-2
x2(x+3)-2
x2x+3-2
x^2x+3-2
Similar expressions
x^2*(x+3)+2
x^2*(x-3)-2

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

Derivative of x^2*(x+3)-2

The solution

You have entered [src]

 2            
x *(x + 3) - 2

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

x^2*(x + 3) - 2

Detail solution

Differentiate $x^{2} \left(x + 3\right) - 2$ term by term:
1. 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: $x^{2} + 2 x \left(x + 3\right)$
2. The derivative of the constant $-2$ is zero.
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)-2