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Derivative of:
Derivative of 2x²
Derivative of x^2*sqrt(1-x^2)
Derivative of 2*sqrt(x^3)
Derivative of (x+1)*(x+2)^2*(x+3)^3
Identical expressions
x^ three -2x^ six +6x
x cubed minus 2x to the power of 6 plus 6x
x to the power of three minus 2x to the power of six plus 6x
x3-2x6+6x
x³-2x⁶+6x
x to the power of 3-2x to the power of 6+6x
Similar expressions
x^3+2x^6+6x
x^3-2x^6-6x

The derivative of the function/ x^3-2x^6+6x

Derivative of x^3-2x^6+6x

The solution

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 3      6      
x  - 2*x  + 6*x

$$6 x + \left(- 2 x^{6} + x^{3}\right)$$

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Detail solution

Differentiate $6 x + \left(- 2 x^{6} + x^{3}\right)$ term by term:
1. Differentiate $- 2 x^{6} + x^{3}$ 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: $x^{6}$ goes to $6 x^{5}$
    So, the result is: $- 12 x^{5}$
  The result is: $- 12 x^{5} + 3 x^{2}$
2. The derivative of a constant times a function is the constant times the derivative of the function.
  1. Apply the power rule: $x$ goes to $1$
  So, the result is: $6$
The result is: $- 12 x^{5} + 3 x^{2} + 6$

The answer is:

$- 12 x^{5} + 3 x^{2} + 6$

The graph

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The first derivative [src]

        5      2
6 - 12*x  + 3*x

$$- 12 x^{5} + 3 x^{2} + 6$$

Simplify

The second derivative [src]

    /        3\
6*x*\1 - 10*x /

$$6 x \left(1 - 10 x^{3}\right)$$

Simplify

The third derivative [src]

  /        3\
6*\1 - 40*x /

$$6 \left(1 - 40 x^{3}\right)$$

Simplify

The graph

Derivative of x^3-2x^6+6x