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Derivative of:
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Derivative of x²-2
Derivative of tan(3*x^4-13)^(5)
Integral of d{x}:
cos^2x/2
Identical expressions
cos^ two x/2
co sinus of e of squared x divide by 2
co sinus of e of to the power of two x divide by 2
cos2x/2
cos²x/2
cos to the power of 2x/2
cos^2x divide by 2

The derivative of the function/ cos^2x/2

Derivative of cos^2x/2

The solution

You have entered [src]

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

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

cos(x)^2/2

Detail solution

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

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-cos(x)*sin(x)

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

Simplify

The second derivative [src]

   2         2   
sin (x) - cos (x)

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

Simplify

The third derivative [src]

4*cos(x)*sin(x)

$$4 \sin{\left(x \right)} \cos{\left(x \right)}$$

Simplify

The graph

Derivative of cos^2x/2