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Derivative of:
Derivative of (x^2-4)^3
Derivative of -x^3+(1/2)*x^2-x+1
Derivative of x^3-2x^4
Derivative of (x^2+8)/(x-1)
Identical expressions
x^ three -2x^ four
x cubed minus 2x to the power of 4
x to the power of three minus 2x to the power of four
x3-2x4
x³-2x⁴
x to the power of 3-2x to the power of 4
Similar expressions
x^3+2x^4

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

Derivative of x^3-2x^4

The solution

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 3      4
x  - 2*x

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

x^3 - 2*x^4

Detail solution

Differentiate $- 2 x^{4} + x^{3}$ term by term:
1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Apply the power rule: $x^{4}$ goes to $4 x^{3}$
  So, the result is: $- 8 x^{3}$
The result is: $- 8 x^{3} + 3 x^{2}$
Now simplify:

$x^{2} \left(3 - 8 x\right)$

The answer is:

$x^{2} \left(3 - 8 x\right)$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

     3      2
- 8*x  + 3*x

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

Simplify

The second derivative [src]

6*x*(1 - 4*x)

$$6 x \left(1 - 4 x\right)$$

Simplify

The third derivative [src]

6*(1 - 8*x)

$$6 \left(1 - 8 x\right)$$

Simplify

The graph

Derivative of x^3-2x^4