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Derivative of:
Derivative of -e^x
Derivative of 1/2*sqrt(x)
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Derivative of x^5-5*x^3-20*x
Identical expressions
four *x^ three - sixteen *x
4 multiply by x cubed minus 16 multiply by x
four multiply by x to the power of three minus sixteen multiply by x
4*x3-16*x
4*x³-16*x
4*x to the power of 3-16*x
4x^3-16x
4x3-16x
Similar expressions
4*x^3+16*x

The derivative of the function/ 4*x^3-16*x

Derivative of 4x^3-16x

The solution

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   3       
4*x  - 16*x

$$4 x^{3} - 16 x$$

4*x^3 - 16*x

Detail solution

Differentiate $4 x^{3} - 16 x$ 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: $x^{3}$ goes to $3 x^{2}$
  So, the result is: $12 x^{2}$
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: $-16$
The result is: $12 x^{2} - 16$

The answer is:

$12 x^{2} - 16$

The graph

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The first derivative [src]

          2
-16 + 12*x

$$12 x^{2} - 16$$

Simplify

The second derivative [src]

24*x

$$24 x$$

Simplify

The third derivative [src]

$$24$$

Simplify