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

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Graphing y =:
2*cos(x)-cos(2*x)
Identical expressions
two *cos(x)-cos(two *x)
2 multiply by co sinus of e of (x) minus co sinus of e of (2 multiply by x)
two multiply by co sinus of e of (x) minus co sinus of e of (two multiply by x)
2cos(x)-cos(2x)
2cosx-cos2x
Similar expressions
2*cos(x)+cos(2*x)
3*(2cosx-cos2x)
3(2cos(x)-cos(2x))
2(cosx-cos2x)
2*cosx-cos(2*x)

The derivative of the function/ 2*cos(x)-cos(2*x)

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

The solution

You have entered [src]

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

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

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

Detail solution

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.
      1. 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: $- 2 \sin{\left(x \right)} + 2 \sin{\left(2 x \right)}$

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

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

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

Simplify

The graph

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