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Derivative of:
Derivative of e^2*x
Derivative of cos(x)^2
Derivative of x^sin(x)
Derivative of sin(x^3)
Identical expressions
(three / two)x-(one / eight)x^ three
(3 divide by 2)x minus (1 divide by 8)x cubed
(three divide by two)x minus (one divide by eight)x to the power of three
(3/2)x-(1/8)x3
3/2x-1/8x3
(3/2)x-(1/8)x³
(3/2)x-(1/8)x to the power of 3
3/2x-1/8x^3
(3 divide by 2)x-(1 divide by 8)x^3
Similar expressions
(3/2)x+(1/8)x^3

The derivative of the function/ (3/2)x-(1/8)x^3

Derivative of (3/2)x-(1/8)x^3

The solution

You have entered [src]

       3
3*x   x 
--- - --
 2    8

$$- \frac{x^{3}}{8} + \frac{3 x}{2}$$

3*x/2 - x^3/8

Detail solution

Differentiate $- \frac{x^{3}}{8} + \frac{3 x}{2}$ 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: $x$ goes to $1$
  So, the result is: $\frac{3}{2}$
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: $- \frac{3 x^{2}}{8}$
The result is: $\frac{3}{2} - \frac{3 x^{2}}{8}$

The answer is:

$\frac{3}{2} - \frac{3 x^{2}}{8}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

       2
3   3*x 
- - ----
2    8

$$\frac{3}{2} - \frac{3 x^{2}}{8}$$

Simplify

The second derivative [src]

-3*x
----
 4

$$- \frac{3 x}{4}$$

Simplify

The third derivative [src]

-3/4

$$- \frac{3}{4}$$

Simplify