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Derivative of:
Derivative of (-1)/cos(x)
Derivative of (1-x^2)^(1/2)
Derivative of x-sin(x)
Derivative of x^(3*x)
Graphing y =:
x^4-3x^3+x^2
Identical expressions
y=x^ four - three x^3+x^ two
y equally x to the power of 4 minus 3x cubed plus x squared
y equally x to the power of four minus three x cubed plus x to the power of two
y=x4-3x3+x2
y=x⁴-3x³+x²
y=x to the power of 4-3x to the power of 3+x to the power of 2
Similar expressions
y=x^4+3x^3+x^2
y=x^4-3x^3-x^2

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

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

The solution

You have entered [src]

 4      3    2
x  - 3*x  + x

$$x^{2} + \left(x^{4} - 3 x^{3}\right)$$

Transform

Detail solution

Differentiate $x^{2} + \left(x^{4} - 3 x^{3}\right)$ term by term:
1. Differentiate $x^{4} - 3 x^{3}$ term by term:
  1. Apply the power rule: $x^{4}$ goes to $4 x^{3}$
  2. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$
    So, the result is: $- 9 x^{2}$
  The result is: $4 x^{3} - 9 x^{2}$
2. Apply the power rule: $x^{2}$ goes to $2 x$
The result is: $4 x^{3} - 9 x^{2} + 2 x$
Now simplify:

$x \left(4 x^{2} - 9 x + 2\right)$

The answer is:

$x \left(4 x^{2} - 9 x + 2\right)$

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 /

$$2 \left(6 x^{2} - 9 x + 1\right)$$

Simplify

The third derivative [src]

6*(-3 + 4*x)

$$6 \left(4 x - 3\right)$$

Simplify

The graph

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