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

Derivative of 6x^3-9x+2

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The solution

You have entered [src] 
   3          
6*x  - 9*x + 2
6x3−9x+26 x^{3} - 9 x + 2 
d /   3          \
--\6*x  - 9*x + 2/
dx
ddx(6x3−9x+2)\frac{d}{d x} \left(6 x^{3} - 9 x + 2\right)
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Detail solution

  1. Differentiate 6x3−9x+26 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: x3x^{3} goes to 3x23 x^{2}

      So, the result is: 18x218 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: xx goes to 11

        So, the result is: 99

      So, the result is: −9-9

    3. The derivative of the constant 22 is zero.

    The result is: 18x2−918 x^{2} - 9

The answer is:

18x2−918 x^{2} - 9

The graph
02468-8-6-4-2-1010-1000010000
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
         2
-9 + 18*x
18x2−918 x^{2} - 9
Simplify
The second derivative [src] 
36*x
36x36 x
Simplify
The third derivative [src] 
36
3636
Simplify
The graph
Derivative of 6x^3-9x+2
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