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

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

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

The solution

You have entered [src]

   4      2    
- x  + 2*x  + 3

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

-x^4 + 2*x^2 + 3

Detail solution

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

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

The answer is:

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

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 /

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

Simplify

The third derivative [src]

-24*x

$$- 24 x$$

Simplify