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Derivative of:
Derivative of e^(7*x)
Derivative of cos(x/3)
Derivative of √x
Derivative of xcos(x)
Identical expressions
six *x-((x^ three)/ eight)
6 multiply by x minus ((x cubed ) divide by 8)
six multiply by x minus ((x to the power of three) divide by eight)
6*x-((x3)/8)
6*x-x3/8
6*x-((x³)/8)
6*x-((x to the power of 3)/8)
6x-((x^3)/8)
6x-((x3)/8)
6x-x3/8
6x-x^3/8
6*x-((x^3) divide by 8)
Similar expressions
6*x+((x^3)/8)

The derivative of the function/ 6*x-((x^3)/8)

Derivative of 6*x-((x^3)/8)

The solution

You have entered [src]

$$- \frac{x^{3}}{8} + 6 x$$

  /       3\
d |      x |
--|6*x - --|
dx\      8 /

$$\frac{d}{d x} \left(- \frac{x^{3}}{8} + 6 x\right)$$

Transform

Detail solution

Differentiate $- \frac{x^{3}}{8} + 6 x$ 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: $6$
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: $\frac{3 x^{2}}{8}$
  So, the result is: $- \frac{3 x^{2}}{8}$
The result is: $6 - \frac{3 x^{2}}{8}$

The answer is:

$6 - \frac{3 x^{2}}{8}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

       2
    3*x 
6 - ----
     8

$$- \frac{3 x^{2}}{8} + 6$$

Simplify

The second derivative [src]

-3*x
----
 4

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

Simplify

The third derivative [src]

-3/4

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

Simplify

The graph

Derivative of 6*x-((x^3)/8)