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

Derivative of y=x^4-3x^3+x^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  - 3*x  + x  - 1
$$x^{4} - 3 x^{3} + x^{2} - 1$$ 
d / 4      3    2    \
--\x  - 3*x  + x  - 1/
dx
$$\frac{d}{d x} \left(x^{4} - 3 x^{3} + x^{2} - 1\right)$$
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. Apply the power rule: goes to

    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
- 9*x  + 2*x + 4*x
$$4 x^{3} - 9 x^{2} + 2 x$$
Simplify
The second derivative [src] 
  /             2\
2*\1 - 9*x + 6*x /
$$2 \cdot \left(6 x^{2} - 9 x + 1\right)$$
Simplify
The third derivative [src] 
6*(-3 + 4*x)
$$6 \cdot \left(4 x - 3\right)$$
Simplify
The graph
Derivative of y=x^4-3x^3+x^2-1
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