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Derivative of:
Derivative of 2/e^x
Derivative of x^3*lnx
Derivative of 2/(x+1)
Derivative of y=2x-1
Identical expressions
y=cos^ two *x/ three
y equally co sinus of e of squared multiply by x divide by 3
y equally co sinus of e of to the power of two multiply by x divide by three
y=cos2*x/3
y=cos²*x/3
y=cos to the power of 2*x/3
y=cos^2x/3
y=cos2x/3
y=cos^2*x divide by 3

The derivative of the function/ y=cos^2*x/3

Derivative of y=cos^2*x/3

The solution

You have entered [src]

   2   
cos (x)
-------
   3

$$\frac{\cos^{2}{\left(x \right)}}{3}$$

cos(x)^2/3

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: $- \frac{2 \sin{\left(x \right)} \cos{\left(x \right)}}{3}$
Now simplify:

$- \frac{\sin{\left(2 x \right)}}{3}$

The answer is:

$- \frac{\sin{\left(2 x \right)}}{3}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-2*cos(x)*sin(x)
----------------
       3

$$- \frac{2 \sin{\left(x \right)} \cos{\left(x \right)}}{3}$$

Simplify

The second derivative [src]

  /   2         2   \
2*\sin (x) - cos (x)/
---------------------
          3

$$\frac{2 \left(\sin^{2}{\left(x \right)} - \cos^{2}{\left(x \right)}\right)}{3}$$

Simplify

The third derivative [src]

8*cos(x)*sin(x)
---------------
       3

$$\frac{8 \sin{\left(x \right)} \cos{\left(x \right)}}{3}$$

Simplify