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Derivative of:
Derivative of (-2)/x^2
Derivative of (cos(x))^sin(x)
Derivative of y=(x+2)²(2x-1)³
Derivative of y=5x-6
Identical expressions
(one +sin(two *x))/ two
(1 plus sinus of (2 multiply by x)) divide by 2
(one plus sinus of (two multiply by x)) divide by two
(1+sin(2x))/2
1+sin2x/2
(1+sin(2*x)) divide by 2
Similar expressions
(1-sin(2*x))/2

The derivative of the function/ (1+sin(2*x))/2

Derivative of (1+sin(2*x))/2

The solution

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

$$\frac{\sin{\left(2 x \right)} + 1}{2}$$

(1 + sin(2*x))/2

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Differentiate $\sin{\left(2 x \right)} + 1$ term by term:
  1. The derivative of the constant $1$ is zero.
  2. Let $u = 2 x$ .
  3. The derivative of sine is cosine:
    
    $\frac{d}{d u} \sin{\left(u \right)} = \cos{\left(u \right)}$
  4. 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:
    
    $2 \cos{\left(2 x \right)}$
  The result is: $2 \cos{\left(2 x \right)}$
So, the result is: $\cos{\left(2 x \right)}$

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

cos(2*x)

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

Simplify

The second derivative [src]

-2*sin(2*x)

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

Simplify

The third derivative [src]

-4*cos(2*x)

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

Simplify

The graph

Derivative of (1+sin(2*x))/2