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Derivative of:
Derivative of 4*e^(2*x)
Derivative of 1/3*x^3
Derivative of x^asin(x)
Derivative of x^2+2x
Graphing y =:
3/2x^2-x^3
Identical expressions
three / two x^2-x^ three
3 divide by 2x squared minus x cubed
three divide by two x squared minus x to the power of three
3/2x2-x3
3/2x²-x³
3/2x to the power of 2-x to the power of 3
3 divide by 2x^2-x^3
Similar expressions
3/2x^2+x^3

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

Derivative of 3/2x^2-x^3

The solution

You have entered [src]

   2     
3*x     3
---- - x 
 2

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

3*x^2/2 - x^3

Detail solution

Differentiate $- x^{3} + \frac{3 x^{2}}{2}$ 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: $3 x$
2. 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: $- 3 x^{2}$
The result is: $- 3 x^{2} + 3 x$
Now simplify:

$3 x \left(1 - x\right)$

The answer is:

3 x \left(1 - x\right)

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

     2      
- 3*x  + 3*x

- 3 x^{2} + 3 x

Simplify

The second derivative [src]

3*(1 - 2*x)

3 \left(1 - 2 x\right)

Simplify

The third derivative [src]

-6

-6

Simplify