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Derivative of:
Derivative of 4x^2
Derivative of 7
Derivative of coth(x)/tanh(x)
Derivative of 2^x^2
Factor polynomial:
x^4-x^2+1
Factor squared:
x^4-x^2+1
Graphing y =:
x^4-x^2+1
Identical expressions
x^ four -x^ two + one
x to the power of 4 minus x squared plus 1
x to the power of four minus x to the power of two plus one
x4-x2+1
x⁴-x²+1
x to the power of 4-x to the power of 2+1
Similar expressions
x^4-x^2-1
x^4+x^2+1

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

Derivative of x^4-x^2+1

The solution

You have entered [src]

 4    2    
x  - x  + 1

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

x^4 - x^2 + 1

Detail solution

Differentiate $\left(x^{4} - x^{2}\right) + 1$ term by term:
1. Differentiate $x^{4} - x^{2}$ 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: $x^{2}$ goes to $2 x$
    So, the result is: $- 2 x$
  The result is: $4 x^{3} - 2 x$
2. The derivative of the constant $1$ is zero.
The result is: $4 x^{3} - 2 x$

The answer is:

$4 x^{3} - 2 x$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

          3
-2*x + 4*x

$$4 x^{3} - 2 x$$

Simplify

The second derivative [src]

  /        2\
2*\-1 + 6*x /

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

Simplify

The third derivative [src]

24*x

$$24 x$$

Simplify

The graph

Derivative of x^4-x^2+1