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Derivative of:
Derivative of 2*cos(3*x)
Derivative of 1^3*sqrt(x)
Derivative of (x+4)/(x-1)
Derivative of (x-3)^4
Identical expressions
x^ two - one / two x^2
x squared minus 1 divide by 2x squared
x to the power of two minus one divide by two x squared
x2-1/2x2
x²-1/2x²
x to the power of 2-1/2x to the power of 2
x^2-1 divide by 2x^2
Similar expressions
x^2+1/2x^2

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

Derivative of x^2-1/2x^2

The solution

You have entered [src]

$$- \frac{x^{2}}{2} + x^{2}$$

  /      2\
d | 2   x |
--|x  - --|
dx\     2 /

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

Transform

Detail solution

Differentiate $- \frac{x^{2}}{2} + x^{2}$ term by term:
1. Apply the power rule: $x^{2}$ goes to $2 x$
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: $x$
  So, the result is: $- x$
The result is: $x$

The answer is:

$x$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

$$x$$

Simplify

The second derivative [src]

$$1$$

Simplify

The third derivative [src]

$$0$$

Simplify

The graph

Derivative of x^2-1/2x^2