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Derivative of:
Derivative of sin(x/3)^(2)*cot(x/2)
Derivative of -sin2x
Derivative of e^cos(x)
Derivative of ln(x+3)^3
Graphing y =:
x^4-4x^3
Identical expressions
x^ four -4x^ three
x to the power of 4 minus 4x cubed
x to the power of four minus 4x to the power of three
x4-4x3
x⁴-4x³
x to the power of 4-4x to the power of 3
Similar expressions
x^4-4*x^3+20
x^4+4x^3

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

Derivative of x^4-4x^3

The solution

You have entered [src]

 4      3
x  - 4*x

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

x^4 - 4*x^3

Detail solution

Differentiate $x^{4} - 4 x^{3}$ term by term:
1. Apply the power rule: $x^{4}$ goes to $4 x^{3}$
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: $- 12 x^{2}$
The result is: $4 x^{3} - 12 x^{2}$
Now simplify:

$4 x^{2} \left(x - 3\right)$

The answer is:

$4 x^{2} \left(x - 3\right)$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

      2      3
- 12*x  + 4*x

$$4 x^{3} - 12 x^{2}$$

Simplify

The second derivative [src]

12*x*(-2 + x)

$$12 x \left(x - 2\right)$$

Simplify

The third derivative [src]

24*(-1 + x)

$$24 \left(x - 1\right)$$

Simplify

The graph

Derivative of x^4-4x^3