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Derivative of:
Derivative of cos(sqrt(x))
Derivative of cos(1/x)
Derivative of 2*x-1
Derivative of 2x+1
Identical expressions
zero .5x^ two -2x^ three
0.5x squared minus 2x cubed
zero .5x to the power of two minus 2x to the power of three
0.5x2-2x3
0.5x²-2x³
0.5x to the power of 2-2x to the power of 3
Similar expressions
0.5x^2+2x^3

The derivative of the function/ 0.5x^2-2x^3

Derivative of 0.5x^2-2x^3

The solution

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$$- 2 x^{3} + \frac{x^{2}}{2}$$

  / 2       \
d |x       3|
--|-- - 2*x |
dx\2        /

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

Transform

Detail solution

Differentiate $- 2 x^{3} + \frac{x^{2}}{2}$ 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: $x^{2}$ goes to $2 x$
  So, the result is: $x$
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: $x^{3}$ goes to $3 x^{2}$
    So, the result is: $6 x^{2}$
  So, the result is: $- 6 x^{2}$
The result is: $- 6 x^{2} + x$
Now simplify:

$x \left(1 - 6 x\right)$

The answer is:

$x \left(1 - 6 x\right)$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

       2
x - 6*x

$$- 6 x^{2} + x$$

Simplify

The second derivative [src]

1 - 12*x

$$1 - 12 x$$

Simplify

The third derivative [src]

-12

$$-12$$

Simplify

The graph

Derivative of 0.5x^2-2x^3