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The derivative of the function/ -6(-6x³-6×+2)⅙

Derivative of -6(-6x³-6×+2)⅙

The solution

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

$$\frac{\left(-1\right) 6 \left(\left(- 6 x^{3} - 6 x\right) + 2\right)}{6}$$

(-6*(-6*x^3 - 6*x + 2))/6

Detail solution

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. Differentiate $\left(- 6 x^{3} - 6 x\right) + 2$ term by term:
    1. Differentiate $- 6 x^{3} - 6 x$ term by term:
      1. The derivative of a constant times a function is the constant times the derivative of the function.
        
        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.
        
        Apply the power rule: $x$ goes to $1$
        
        So, the result is: $-6$
      The result is: $- 18 x^{2} - 6$
    2. The derivative of the constant $2$ is zero.
    The result is: $- 18 x^{2} - 6$
  So, the result is: $108 x^{2} + 36$
So, the result is: $18 x^{2} + 6$

The answer is:

$18 x^{2} + 6$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

        2
6 + 18*x

$$18 x^{2} + 6$$

Simplify

The second derivative [src]

36*x

$$36 x$$

Simplify

The third derivative [src]

$$36$$

Simplify