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Derivative of -x^3+3x^2+4

Function f() - derivative -N order at the point
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The solution

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   3      2    
- x  + 3*x  + 4
(x3+3x2)+4\left(- x^{3} + 3 x^{2}\right) + 4
-x^3 + 3*x^2 + 4
Detail solution
  1. Differentiate (x3+3x2)+4\left(- x^{3} + 3 x^{2}\right) + 4 term by term:

    1. Differentiate x3+3x2- x^{3} + 3 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: 3x2- 3 x^{2}

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

        1. Apply the power rule: x2x^{2} goes to 2x2 x

        So, the result is: 6x6 x

      The result is: 3x2+6x- 3 x^{2} + 6 x

    2. The derivative of the constant 44 is zero.

    The result is: 3x2+6x- 3 x^{2} + 6 x

  2. Now simplify:

    3x(2x)3 x \left(2 - x\right)


The answer is:

3x(2x)3 x \left(2 - x\right)

The graph
02468-8-6-4-2-1010-20002000
The first derivative [src]
     2      
- 3*x  + 6*x
3x2+6x- 3 x^{2} + 6 x
The second derivative [src]
6*(1 - x)
6(1x)6 \left(1 - x\right)
The third derivative [src]
-6
6-6