Mister Exam

Derivative of y=x³-3x²+3x+1

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

The graph:

from to

Piecewise:

The solution

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

    1. Apply the power rule: goes to

    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: goes to

        So, the result is:

      So, the result is:

    3. 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:

    4. The derivative of the constant is zero.

    The result is:


The answer is:

The graph
The first derivative [src]
             2
3 - 6*x + 3*x 
$$3 x^{2} - 6 x + 3$$
The second derivative [src]
6*(-1 + x)
$$6 \left(x - 1\right)$$
The third derivative [src]
6
$$6$$
The graph
Derivative of y=x³-3x²+3x+1