Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of 1/x
Derivative of (cos(x))^2
Derivative of xlnx
Derivative of ln(2x^3+3x^2)
Integral of d{x}:
(cos(x))^2
Canonical form:
(cos(x))^2
Graphing y =:
(cos(x))^2
Identical expressions
(cos(x))^ two
( co sinus of e of (x)) squared
( co sinus of e of (x)) to the power of two
(cos(x))2
cosx2
(cos(x))²
(cos(x)) to the power of 2
cosx^2
Similar expressions
(-1)/(cos(x)^2*sin(x)^(2*x))
sinx^2/cosx^2
cos(x^2+1)
(arccosx^2)/(1-x^4)
arcctg(x+2)*ln(cos(x^2+1))
(cosx)^2

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

Derivative of (cos(x))^2

The solution

You have entered [src]

   2   
cos (x)

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

d /   2   \
--\cos (x)/
dx

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

Transform

Detail solution

Let $u = \cos{\left(x \right)}$ .
Apply the power rule: $u^{2}$ goes to $2 u$
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:

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

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

8*cos(x)*sin(x)

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

Simplify

The graph

Derivative of (cos(x))^2