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Identical expressions
three (2cos(x)-cos(2x))
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three (2 co sinus of e of (x) minus co sinus of e of (2x))
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Similar expressions
3*(2cosx-cos2x)
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The derivative of the function/ 3(2cos(x)-cos(2x))

Derivative of 3(2cos(x)-cos(2x))

The solution

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3*(2*cos(x) - cos(2*x))

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

3*(2*cos(x) - cos(2*x))

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Differentiate $2 \cos{\left(x \right)} - \cos{\left(2 x \right)}$ term by term:
  1. The derivative of a constant times a function is the constant times the derivative of the function.
    1. The derivative of cosine is negative sine:
      
      $\frac{d}{d x} \cos{\left(x \right)} = - \sin{\left(x \right)}$
    So, the result is: $- 2 \sin{\left(x \right)}$
  2. The derivative of a constant times a function is the constant times the derivative of the function.
    1. Let $u = 2 x$ .
    2. The derivative of cosine is negative sine:
      
      $\frac{d}{d u} \cos{\left(u \right)} = - \sin{\left(u \right)}$
    3. Then, apply the chain rule. Multiply by $\frac{d}{d x} 2 x$ :
      1. The derivative of a constant times a function is the constant times the derivative of the function.
        
        Apply the power rule: $x$ goes to $1$
        
        So, the result is: $2$
      The result of the chain rule is:
      
      $- 2 \sin{\left(2 x \right)}$
    So, the result is: $2 \sin{\left(2 x \right)}$
  The result is: $- 2 \sin{\left(x \right)} + 2 \sin{\left(2 x \right)}$
So, the result is: $- 6 \sin{\left(x \right)} + 6 \sin{\left(2 x \right)}$

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-6*sin(x) + 6*sin(2*x)

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

Simplify

The second derivative [src]

6*(-cos(x) + 2*cos(2*x))

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

Simplify

The third derivative [src]

6*(-4*sin(2*x) + sin(x))

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

Simplify