Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of cos(x/3)
Derivative of √x
Derivative of xcos(x)
Derivative of y=(x-2)^2
Integral of d{x}:
(1-cos(2x))/2
Identical expressions
(one -cos(two x))/2
(1 minus co sinus of e of (2x)) divide by 2
(one minus co sinus of e of (two x)) divide by 2
1-cos2x/2
(1-cos(2x)) divide by 2
Similar expressions
(1+cos(2x))/2

The derivative of the function/ (1-cos(2x))/2

Derivative of (1-cos(2x))/2

The solution

You have entered [src]

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

$$\frac{1 - \cos{\left(2 x \right)}}{2}$$

(1 - cos(2*x))/2

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Differentiate $1 - \cos{\left(2 x \right)}$ term by term:
  1. The derivative of the constant $1$ 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.
        
        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: $2 \sin{\left(2 x \right)}$
So, 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