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Derivative of:
Derivative of y=4sinx+9
Derivative of x^4-2x^2+1
Derivative of cos(100*x)
Derivative of (x-1)²
Graphing y =:
x^4-2x^2+1
Identical expressions
x^ four - two x^2+ one
x to the power of 4 minus 2x squared plus 1
x to the power of four minus two x squared plus one
x4-2x2+1
x⁴-2x²+1
x to the power of 4-2x to the power of 2+1
Similar expressions
x^4+2x^2+1
x^4-2*x^2+1
x^4-2x^2-1

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

Derivative of x^4-2x^2+1

The solution

You have entered [src]

 4      2    
x  - 2*x  + 1

$$x^{4} - 2 x^{2} + 1$$

d / 4      2    \
--\x  - 2*x  + 1/
dx

$$\frac{d}{d x} \left(x^{4} - 2 x^{2} + 1\right)$$

Transform

Detail solution

Differentiate $x^{4} - 2 x^{2} + 1$ 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. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Apply the power rule: $x^{2}$ goes to $2 x$
    So, the result is: $4 x$
  So, the result is: $- 4 x$
3. The derivative of the constant $1$ is zero.
The result is: $4 x^{3} - 4 x$
Now simplify:

$4 x \left(x^{2} - 1\right)$

The answer is:

$4 x \left(x^{2} - 1\right)$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

          3
-4*x + 4*x

$$4 x^{3} - 4 x$$

Simplify

The second derivative [src]

  /        2\
4*\-1 + 3*x /

$$4 \cdot \left(3 x^{2} - 1\right)$$

Simplify

The third derivative [src]

24*x

$$24 x$$

Simplify

The graph

Derivative of x^4-2x^2+1