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Identical expressions
x^ three -6x^ two -9x
x cubed minus 6x squared minus 9x
x to the power of three minus 6x to the power of two minus 9x
x3-6x2-9x
x³-6x²-9x
x to the power of 3-6x to the power of 2-9x
Similar expressions
x^3+6x^2-9x
x^3-6x^2+9x

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

Derivative of x^3-6x^2-9x

The solution

You have entered [src]

 3      2      
x  - 6*x  - 9*x

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

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

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

Transform

Detail solution

Differentiate $x^{3} - 6 x^{2} - 9 x$ term by term:
1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$
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: $x^{2}$ goes to $2 x$
    So, the result is: $12 x$
  So, the result is: $- 12 x$
3. 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: $-9$
The result is: $3 x^{2} - 12 x - 9$

The answer is:

$3 x^{2} - 12 x - 9$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

               2
-9 - 12*x + 3*x

$$3 x^{2} - 12 x - 9$$

Simplify

The second derivative [src]

6*(-2 + x)

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

Simplify

The third derivative [src]

$$6$$

Simplify

The graph

Derivative of x^3-6x^2-9x