Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of x*2^x
Derivative of (x^2)/36
Derivative of x^2/log(x)
Derivative of e^(sin(x)-2*x^3)
Graphing y =:
x^2(x-3)
Identical expressions
x^ two (x- three)
x squared (x minus 3)
x to the power of two (x minus three)
x2(x-3)
x2x-3
x²(x-3)
x to the power of 2(x-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

You have entered [src]

 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)