Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of e^2*x
Derivative of cos(x)^2
Derivative of x^sin(x)
Derivative of sin(x^3)
Integral of d{x}:
x^3*(x-2)
Identical expressions
y=x^ three *(x- two)
y equally x cubed multiply by (x minus 2)
y equally x to the power of three multiply by (x minus two)
y=x3*(x-2)
y=x3*x-2
y=x³*(x-2)
y=x to the power of 3*(x-2)
y=x^3(x-2)
y=x3(x-2)
y=x3x-2
y=x^3x-2
Similar expressions
y=x^3*(x+2)

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

Derivative of y=x^3*(x-2)

The solution

You have entered [src]

 3        
x *(x - 2)

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

x^3*(x - 2)

Detail solution

Apply the product rule:

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

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

$x^{2} \left(4 x - 6\right)$

The answer is:

$x^{2} \left(4 x - 6\right)$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

6*x*(-2 + 2*x)

$$6 x \left(2 x - 2\right)$$

Simplify

The third derivative [src]

12*(-1 + 2*x)

$$12 \left(2 x - 1\right)$$

Simplify

The graph

Derivative of y=x^3*(x-2)