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

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

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

The solution

You have entered [src]

 4      2    
x  - 4*x  + 3

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

x^4 - 4*x^2 + 3

Detail solution

Differentiate $\left(x^{4} - 4 x^{2}\right) + 3$ term by term:
1. Differentiate $x^{4} - 4 x^{2}$ 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: $- 8 x$
  The result is: $4 x^{3} - 8 x$
2. The derivative of the constant $3$ is zero.
The result is: $4 x^{3} - 8 x$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

          3
-8*x + 4*x

$$4 x^{3} - 8 x$$

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

24*x

$$24 x$$

Simplify