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Derivative of f(x)=2x³+3x²-12x-3

Function f() - derivative -N order at the point
v

The graph:

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Piecewise:

The solution

You have entered [src]
   3      2           
2*x  + 3*x  - 12*x - 3
$$\left(- 12 x + \left(2 x^{3} + 3 x^{2}\right)\right) - 3$$
2*x^3 + 3*x^2 - 12*x - 3
Detail solution
  1. Differentiate term by term:

    1. Differentiate term by term:

      1. Differentiate 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: goes to

          So, the result is:

        2. The derivative of a constant times a function is the constant times the derivative of the function.

          1. Apply the power rule: goes to

          So, the result is:

        The result is:

      2. The derivative of a constant times a function is the constant times the derivative of the function.

        1. Apply the power rule: goes to

        So, the result is:

      The result is:

    2. The derivative of the constant is zero.

    The result is:


The answer is:

The graph
The first derivative [src]
               2
-12 + 6*x + 6*x 
$$6 x^{2} + 6 x - 12$$
The second derivative [src]
6*(1 + 2*x)
$$6 \left(2 x + 1\right)$$
The third derivative [src]
12
$$12$$