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

Derivative of 3x^2-6x+6

The solution

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   2          
3*x  - 6*x + 6

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

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

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

Transform

Detail solution

Differentiate $3 x^{2} - 6 x + 6$ 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: $x^{2}$ goes to $2 x$
  So, the result is: $6 x$
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: $6$
  So, the result is: $-6$
3. The derivative of the constant $6$ is zero.
The result is: $6 x - 6$

The answer is:

$6 x - 6$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-6 + 6*x

$$6 x - 6$$

Simplify

The second derivative [src]

$$6$$

Simplify

The third derivative [src]

$$0$$

Simplify

The graph

Derivative of 3x^2-6x+6