Mister Exam

Lang:

The derivative of the function/ 6x^3-9x+2

Derivative of 6x^3-9x+2

The solution

You have entered [src]

   3          
6*x  - 9*x + 2

$$6 x^{3} - 9 x + 2$$

d /   3          \
--\6*x  - 9*x + 2/
dx

$$\frac{d}{d x} \left(6 x^{3} - 9 x + 2\right)$$

Transform

Detail solution

Differentiate $6 x^{3} - 9 x + 2$ term by term:
1. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$
  So, the result is: $18 x^{2}$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Apply the power rule: $x$ goes to $1$
    So, the result is: $9$
  So, the result is: $-9$
3. The derivative of the constant $2$ is zero.
The result is: $18 x^{2} - 9$

The answer is:

$18 x^{2} - 9$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

         2
-9 + 18*x

$$18 x^{2} - 9$$

Simplify

The second derivative [src]

36*x

$$36 x$$

Simplify

The third derivative [src]

$$36$$

Simplify

The graph

Derivative of 6x^3-9x+2