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Derivative of:
Derivative of 5
Derivative of 5/x
Derivative of 4
Derivative of cos(2*x)
Identical expressions
two x^ six -2x^2
2x to the power of 6 minus 2x squared
two x to the power of six minus 2x squared
2x6-2x2
2x⁶-2x²
2x to the power of 6-2x to the power of 2
Similar expressions
2x^6+2x^2

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

Derivative of 2x^6-2x^2

The solution

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   6      2
2*x  - 2*x

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

d /   6      2\
--\2*x  - 2*x /
dx

$$\frac{d}{d x} \left(2 x^{6} - 2 x^{2}\right)$$

Transform

Detail solution

Differentiate $2 x^{6} - 2 x^{2}$ 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: $x^{6}$ goes to $6 x^{5}$
  So, the result is: $12 x^{5}$
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: $x^{2}$ goes to $2 x$
    So, the result is: $4 x$
  So, the result is: $- 4 x$
The result is: $12 x^{5} - 4 x$

The answer is:

$12 x^{5} - 4 x$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

           5
-4*x + 12*x

$$12 x^{5} - 4 x$$

Simplify

The second derivative [src]

  /         4\
4*\-1 + 15*x /

$$4 \cdot \left(15 x^{4} - 1\right)$$

Simplify

3-th derivative [src]

     3
240*x

$$240 x^{3}$$

Simplify

The third derivative [src]

     3
240*x

$$240 x^{3}$$

Simplify

The graph

Derivative of 2x^6-2x^2