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x^4-4x^3

Derivative of x^4-4x^3

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

The graph:

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Piecewise:

The solution

You have entered [src]
 4      3
x  - 4*x 
x44x3x^{4} - 4 x^{3}
x^4 - 4*x^3
Detail solution
  1. Differentiate x44x3x^{4} - 4 x^{3} term by term:

    1. Apply the power rule: x4x^{4} goes to 4x34 x^{3}

    2. 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: 12x2- 12 x^{2}

    The result is: 4x312x24 x^{3} - 12 x^{2}

  2. Now simplify:

    4x2(x3)4 x^{2} \left(x - 3\right)


The answer is:

4x2(x3)4 x^{2} \left(x - 3\right)

The graph
02468-8-6-4-2-1010-2000020000
The first derivative [src]
      2      3
- 12*x  + 4*x 
4x312x24 x^{3} - 12 x^{2}
The second derivative [src]
12*x*(-2 + x)
12x(x2)12 x \left(x - 2\right)
The third derivative [src]
24*(-1 + x)
24(x1)24 \left(x - 1\right)
The graph
Derivative of x^4-4x^3