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Derivative of:
Derivative of sqrt(x^3)
Derivative of sqrt(x^2)
Derivative of atan(1/x)
Derivative of 3*sin(x)
Graphing y =:
1/4x^4-1/3x^3
Identical expressions
one / four x^4- one / three x^3
1 divide by 4x to the power of 4 minus 1 divide by 3x cubed
one divide by four x to the power of 4 minus one divide by three x cubed
1/4x4-1/3x3
1/4x⁴-1/3x³
1/4x to the power of 4-1/3x to the power of 3
1 divide by 4x^4-1 divide by 3x^3
Similar expressions
1/4x^4+1/3x^3

The derivative of the function/ 1/4x^4-1/3x^3

Derivative of 1/4x^4-1/3x^3

The solution

You have entered [src]

 4    3
x    x 
-- - --
4    3

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

  / 4    3\
d |x    x |
--|-- - --|
dx\4    3 /

$$\frac{d}{d x} \left(\frac{x^{4}}{4} - \frac{x^{3}}{3}\right)$$

Transform

Detail solution

Differentiate $\frac{x^{4}}{4} - \frac{x^{3}}{3}$ 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: $x^{4}$ goes to $4 x^{3}$
  So, the result is: $x^{3}$
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: $x^{2}$
  So, the result is: $- x^{2}$
The result is: $x^{3} - x^{2}$
Now simplify:

$x^{2} \left(x - 1\right)$

The answer is:

$x^{2} \left(x - 1\right)$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

 3    2
x  - x

$$x^{3} - x^{2}$$

Simplify

The second derivative [src]

x*(-2 + 3*x)

$$x \left(3 x - 2\right)$$

Simplify

The third derivative [src]

2*(-1 + 3*x)

$$2 \cdot \left(3 x - 1\right)$$

Simplify

The graph

Derivative of 1/4x^4-1/3x^3