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Derivative of:
Derivative of 1/3*x^3-4*x
Derivative of x²-4
Derivative of x^((2*e)^(4*x))
Derivative of (x-1)√x^2-2x+2
Identical expressions
four - zero , five *cos(2x)
4 minus 0,5 multiply by co sinus of e of (2x)
four minus zero , five multiply by co sinus of e of (2x)
4-0,5cos(2x)
4-0,5cos2x
Similar expressions
4+0,5*cos(2x)

The derivative of the function/ 4-0,5*cos(2x)

Derivative of 4-0,5*cos(2x)

The solution

You have entered [src]

    cos(2*x)
4 - --------
       2

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

4 - cos(2*x)/2

Detail solution

Differentiate $4 - \frac{\cos{\left(2 x \right)}}{2}$ term by term:
1. The derivative of the constant $4$ is zero.
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: $\sin{\left(2 x \right)}$
The result is: $\sin{\left(2 x \right)}$

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

sin(2*x)

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

Simplify

The second derivative [src]

2*cos(2*x)

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

Simplify

The third derivative [src]

-4*sin(2*x)

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

Simplify