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

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

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

The solution

You have entered [src]

   4      2    
2*x  - 4*x  + 1

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

2*x^4 - 4*x^2 + 1

Detail solution

Differentiate $\left(2 x^{4} - 4 x^{2}\right) + 1$ term by term:
1. Differentiate $2 x^{4} - 4 x^{2}$ term by term:
  1. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Apply the power rule: $x^{4}$ goes to $4 x^{3}$
    So, the result is: $8 x^{3}$
  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: $- 8 x$
  The result is: $8 x^{3} - 8 x$
2. The derivative of the constant $1$ is zero.
The result is: $8 x^{3} - 8 x$
Now simplify:

$8 x \left(x^{2} - 1\right)$

The answer is:

$8 x \left(x^{2} - 1\right)$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

          3
-8*x + 8*x

$$8 x^{3} - 8 x$$

Simplify

The second derivative [src]

  /        2\
8*\-1 + 3*x /

$$8 \left(3 x^{2} - 1\right)$$

Simplify

The third derivative [src]

48*x

$$48 x$$

Simplify