Mister Exam

Other calculators

x^4-2x^3
The derivative of the function/ x^4-2x^3

Derivative of x^4-2x^3

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 4      3
x  - 2*x
x4−2x3x^{4} - 2 x^{3} 
d / 4      3\
--\x  - 2*x /
dx
ddx(x4−2x3)\frac{d}{d x} \left(x^{4} - 2 x^{3}\right)
Transform
Detail solution

  1. Differentiate x4−2x3x^{4} - 2 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. 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: 6x26 x^{2}

      So, the result is: −6x2- 6 x^{2}

    The result is: 4x3−6x24 x^{3} - 6 x^{2}

  2. Now simplify:

    x2⋅(4x−6)x^{2} \cdot \left(4 x - 6\right)

The answer is:

x2⋅(4x−6)x^{2} \cdot \left(4 x - 6\right)

The graph
02468-8-6-4-2-1010-2000020000
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
     2      3
- 6*x  + 4*x
4x3−6x24 x^{3} - 6 x^{2}
Simplify
The second derivative [src] 
12*x*(-1 + x)
12x(x−1)12 x \left(x - 1\right)
Simplify
The third derivative [src] 
12*(-1 + 2*x)
12⋅(2x−1)12 \cdot \left(2 x - 1\right)
Simplify
The graph
Derivative of x^4-2x^3
    © Mister Exam – Calculator