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y=x^4-4x^3-8x^2+1
The derivative of the function/ y=x^4-4x^3-8x^2+1

Derivative of y=x^4-4x^3-8x^2+1

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 4      3      2    
x  - 4*x  - 8*x  + 1
$$x^{4} - 4 x^{3} - 8 x^{2} + 1$$ 
d / 4      3      2    \
--\x  - 4*x  - 8*x  + 1/
dx
$$\frac{d}{d x} \left(x^{4} - 4 x^{3} - 8 x^{2} + 1\right)$$
Transform
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. 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:

    4. The derivative of the constant is zero.

    The result is:

  2. Now simplify:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
            2      3
-16*x - 12*x  + 4*x
$$4 x^{3} - 12 x^{2} - 16 x$$
Simplify
The second derivative [src] 
  /              2\
4*\-4 - 6*x + 3*x /
$$4 \cdot \left(3 x^{2} - 6 x - 4\right)$$
Simplify
The third derivative [src] 
24*(-1 + x)
$$24 \left(x - 1\right)$$
Simplify
The graph
Derivative of y=x^4-4x^3-8x^2+1
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