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Derivative of:
Derivative of x^4-2x^3
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Graphing y =:
x^4-2x^3
Identical expressions
x^ four -2x^ three
x to the power of 4 minus 2x cubed
x to the power of four minus 2x to the power of three
x4-2x3
x⁴-2x³
x to the power of 4-2x to the power of 3
Similar expressions
x^4+2x^3
y=x^4-2x^3+5x^2-x+12

The derivative of the function/ x^4-2x^3

Derivative of x^4-2x^3

The solution

You have entered [src]

 4      3
x  - 2*x

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

d / 4      3\
--\x  - 2*x /
dx

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

Transform

Detail solution

Differentiate $x^{4} - 2 x^{3}$ 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. 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: $6 x^{2}$
  So, the result is: $- 6 x^{2}$
The result is: $4 x^{3} - 6 x^{2}$
Now simplify:

$x^{2} \cdot \left(4 x - 6\right)$

The answer is:

$x^{2} \cdot \left(4 x - 6\right)$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

     2      3
- 6*x  + 4*x

$$4 x^{3} - 6 x^{2}$$

Simplify

The second derivative [src]

12*x*(-1 + x)

$$12 x \left(x - 1\right)$$

Simplify

The third derivative [src]

12*(-1 + 2*x)

$$12 \cdot \left(2 x - 1\right)$$

Simplify

The graph

Derivative of x^4-2x^3